# Physics equations/07-Work and Energy/Q:lineIntegral/Testbank

## a07energy_lineIntegral_1_v1

Integrate the line integral of, ${\displaystyle {\vec {F}}=9xy{\hat {x}}+9.5y^{3}{\hat {y}}}$, along the y axis from y = 5 to y = 14

 a) 7.33E+04 b) 7.84E+04 c) 8.39E+04 d) 8.98E+04 e) 9.60E+04

copies
===2===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 9.4xy\hat x + 7.5y^3\hat y$, along the y axis from  y = 4 to y = 17}
- a) 1.19E+05
- b) 1.27E+05
- c) 1.36E+05
- d) 1.46E+05
+ e) 1.56E+05
===3===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 8.2xy\hat x + 7.4y^3\hat y$, along the y axis from  y = 5 to y = 12}
- a) 3.25E+04
- b) 3.48E+04
+ c) 3.72E+04
- d) 3.98E+04
- e) 4.26E+04
===4===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 7.4xy\hat x + 9.3y^3\hat y$, along the y axis from  y = 6 to y = 16}
+ a) 1.49E+05
- b) 1.60E+05
- c) 1.71E+05
- d) 1.83E+05
- e) 1.96E+05
===5===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 5.6xy\hat x + 7.9y^3\hat y$, along the y axis from  y = 5 to y = 15}
+ a) 9.88E+04
- b) 1.06E+05
- c) 1.13E+05
- d) 1.21E+05
- e) 1.29E+05
===6===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 7.9xy\hat x + 8.1y^3\hat y$, along the y axis from  y = 5 to y = 12}
- a) 3.32E+04
- b) 3.56E+04
- c) 3.81E+04
+ d) 4.07E+04
- e) 4.36E+04
===7===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 8.9xy\hat x + 6.5y^3\hat y$, along the y axis from  y = 5 to y = 13}
+ a) 4.54E+04
- b) 4.86E+04
- c) 5.20E+04
- d) 5.56E+04
- e) 5.95E+04
===8===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 9xy\hat x + 5.4y^3\hat y$, along the y axis from  y = 3 to y = 19}
- a) 1.54E+05
- b) 1.64E+05
+ c) 1.76E+05
- d) 1.88E+05
- e) 2.01E+05
===9===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 7.9xy\hat x + 9.7y^3\hat y$, along the y axis from  y = 3 to y = 18}
- a) 1.94E+05
- b) 2.08E+05
- c) 2.22E+05
- d) 2.38E+05
+ e) 2.54E+05
===10===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 6.1xy\hat x + 5.9y^3\hat y$, along the y axis from  y = 6 to y = 12}
+ a) 2.87E+04
- b) 3.07E+04
- c) 3.28E+04
- d) 3.51E+04
- e) 3.76E+04
===11===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 6.8xy\hat x + 7y^3\hat y$, along the y axis from  y = 3 to y = 17}
- a) 1.28E+05
- b) 1.36E+05
+ c) 1.46E+05
- d) 1.56E+05
- e) 1.67E+05
===12===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 9.9xy\hat x + 6.1y^3\hat y$, along the y axis from  y = 7 to y = 16}
- a) 7.86E+04
- b) 8.41E+04
- c) 9.00E+04
+ d) 9.63E+04
- e) 1.03E+05
===13===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 6.9xy\hat x + 7.4y^3\hat y$, along the y axis from  y = 3 to y = 18}
- a) 1.69E+05
- b) 1.81E+05
+ c) 1.94E+05
- d) 2.08E+05
- e) 2.22E+05
===14===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 8.3xy\hat x + 8.6y^3\hat y$, along the y axis from  y = 4 to y = 16}
- a) 1.31E+05
+ b) 1.40E+05
- c) 1.50E+05
- d) 1.61E+05
- e) 1.72E+05
===15===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 8.9xy\hat x + 5.4y^3\hat y$, along the y axis from  y = 7 to y = 17}
+ a) 1.10E+05
- b) 1.17E+05
- c) 1.25E+05
- d) 1.34E+05
- e) 1.44E+05
===16===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 9.4xy\hat x + 9.3y^3\hat y$, along the y axis from  y = 6 to y = 18}
- a) 2.11E+05
- b) 2.25E+05
+ c) 2.41E+05
- d) 2.58E+05
- e) 2.76E+05
===17===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 6.9xy\hat x + 5.5y^3\hat y$, along the y axis from  y = 7 to y = 18}
+ a) 1.41E+05
- b) 1.51E+05
- c) 1.61E+05
- d) 1.73E+05
- e) 1.85E+05
===18===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 8.4xy\hat x + 8.3y^3\hat y$, along the y axis from  y = 5 to y = 15}
- a) 9.70E+04
+ b) 1.04E+05
- c) 1.11E+05
- d) 1.19E+05
- e) 1.27E+05
===19===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 7.3xy\hat x + 5.2y^3\hat y$, along the y axis from  y = 5 to y = 11}
+ a) 1.82E+04
- b) 1.95E+04
- c) 2.09E+04
- d) 2.23E+04
- e) 2.39E+04
===20===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 7.8xy\hat x + 8y^3\hat y$, along the y axis from  y = 6 to y = 13}
- a) 4.45E+04
- b) 4.76E+04
- c) 5.10E+04
+ d) 5.45E+04
- e) 5.83E+04
===21===
{<!--a07energy_lineIntegral_1-->Integrate the line integral of, $\vec F = 8.5xy\hat x + 7.5y^3\hat y$, along the y axis from  y = 7 to y = 18}
- a) 1.68E+05
- b) 1.80E+05
+ c) 1.92E+05
- d) 2.06E+05
- e) 2.20E+05


## a07energy_lineIntegral_2_v1

Integrate the function, ${\displaystyle {\vec {F}}=r^{7}\theta ^{9}{\hat {r}}+r^{7}\theta ^{5}{\hat {\theta }}}$ , along the first quadrant of a circle of radius 8

 a) 3.43E+07 b) 3.67E+07 c) 3.93E+07 d) 4.20E+07 e) 4.49E+07

copies
===2===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^6\theta^8\hat r + r^7\theta^ 6\hat \theta$ , along the first quadrant of a circle of radius 5}
- a) 1.15E+06
- b) 1.23E+06
+ c) 1.32E+06
- d) 1.41E+06
- e) 1.51E+06
===3===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^6\theta^6\hat r + r^8\theta^ 7\hat \theta$ , along the first quadrant of a circle of radius 3}
- a) 6.96E+04
- b) 7.44E+04
- c) 7.97E+04
- d) 8.52E+04
+ e) 9.12E+04
===4===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^4\theta^6\hat r + r^7\theta^ 8\hat \theta$ , along the first quadrant of a circle of radius 6}
+ a) 1.09E+07
- b) 1.16E+07
- c) 1.24E+07
- d) 1.33E+07
- e) 1.42E+07
===5===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^8\theta^9\hat r + r^8\theta^ 5\hat \theta$ , along the first quadrant of a circle of radius 6}
- a) 2.06E+07
- b) 2.20E+07
- c) 2.36E+07
+ d) 2.52E+07
- e) 2.70E+07
===6===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^7\theta^8\hat r + r^9\theta^ 4\hat \theta$ , along the first quadrant of a circle of radius 8}
- a) 1.68E+09
- b) 1.79E+09
- c) 1.92E+09
+ d) 2.05E+09
- e) 2.20E+09
===7===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^9\theta^3\hat r + r^8\theta^ 7\hat \theta$ , along the first quadrant of a circle of radius 4}
- a) 1.14E+06
+ b) 1.21E+06
- c) 1.30E+06
- d) 1.39E+06
- e) 1.49E+06
===8===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^5\theta^7\hat r + r^4\theta^ 4\hat \theta$ , along the first quadrant of a circle of radius 9}
- a) 1.06E+05
+ b) 1.13E+05
- c) 1.21E+05
- d) 1.29E+05
- e) 1.38E+05
===9===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^3\theta^4\hat r + r^6\theta^ 5\hat \theta$ , along the first quadrant of a circle of radius 9}
- a) 1.12E+07
+ b) 1.20E+07
- c) 1.28E+07
- d) 1.37E+07
- e) 1.47E+07
===10===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^4\theta^3\hat r + r^6\theta^ 7\hat \theta$ , along the first quadrant of a circle of radius 7}
- a) 3.33E+06
- b) 3.57E+06
+ c) 3.82E+06
- d) 4.08E+06
- e) 4.37E+06
===11===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^3\theta^7\hat r + r^7\theta^ 4\hat \theta$ , along the first quadrant of a circle of radius 4}
- a) 1.02E+05
- b) 1.09E+05
- c) 1.17E+05
+ d) 1.25E+05
- e) 1.34E+05
===12===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^5\theta^4\hat r + r^5\theta^ 8\hat \theta$ , along the first quadrant of a circle of radius 5}
- a) 8.25E+04
- b) 8.83E+04
- c) 9.45E+04
+ d) 1.01E+05
- e) 1.08E+05
===13===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^6\theta^8\hat r + r^8\theta^ 9\hat \theta$ , along the first quadrant of a circle of radius 3}
- a) 1.37E+05
- b) 1.47E+05
- c) 1.57E+05
- d) 1.68E+05
+ e) 1.80E+05
===14===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^8\theta^5\hat r + r^4\theta^ 6\hat \theta$ , along the first quadrant of a circle of radius 4}
- a) 2.63E+03
- b) 2.82E+03
- c) 3.01E+03
- d) 3.23E+03
+ e) 3.45E+03
===15===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^5\theta^3\hat r + r^6\theta^ 6\hat \theta$ , along the first quadrant of a circle of radius 3}
- a) 6.44E+03
- b) 6.89E+03
+ c) 7.37E+03
- d) 7.89E+03
- e) 8.44E+03
===16===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^7\theta^4\hat r + r^5\theta^ 6\hat \theta$ , along the first quadrant of a circle of radius 7}
- a) 3.03E+05
- b) 3.24E+05
- c) 3.46E+05
- d) 3.71E+05
+ e) 3.97E+05
===17===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^9\theta^6\hat r + r^4\theta^ 4\hat \theta$ , along the first quadrant of a circle of radius 7}
- a) 2.45E+04
- b) 2.62E+04
- c) 2.81E+04
- d) 3.00E+04
+ e) 3.21E+04
===18===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^9\theta^4\hat r + r^7\theta^ 8\hat \theta$ , along the first quadrant of a circle of radius 8}
- a) 8.86E+07
- b) 9.48E+07
- c) 1.01E+08
+ d) 1.09E+08
- e) 1.16E+08
===19===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^9\theta^5\hat r + r^8\theta^ 7\hat \theta$ , along the first quadrant of a circle of radius 4}
- a) 1.14E+06
+ b) 1.21E+06
- c) 1.30E+06
- d) 1.39E+06
- e) 1.49E+06
===20===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^7\theta^3\hat r + r^4\theta^ 7\hat \theta$ , along the first quadrant of a circle of radius 3}
- a) 1.05E+03
+ b) 1.13E+03
- c) 1.20E+03
- d) 1.29E+03
- e) 1.38E+03
===21===
{<!--D044a07energy_lineIntegral_2-->Integrate the function, $\vec F = r^6\theta^5\hat r + r^9\theta^ 7\hat \theta$ , along the first quadrant of a circle of radius 3}
- a) 2.09E+05
- b) 2.23E+05
- c) 2.39E+05
- d) 2.56E+05
+ e) 2.74E+05


## a07energy_lineIntegral_3_v1

Integrate the line integral of ${\displaystyle {\vec {F}}=4xy{\hat {x}}+7.7x{\hat {y}}}$ from the origin to the point at x = 2.5 and y = 3.3

 a) 5.93E+01 b) 6.34E+01 c) 6.78E+01 d) 7.26E+01 e) 7.77E+01

copies
===2===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 3xy\hat x + 6.9x\hat y$  from the origin to the point at x = 2.3 and y = 3.8}
- a) 4.70E+01
+ b) 5.03E+01
- c) 5.38E+01
- d) 5.75E+01
- e) 6.16E+01
===3===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 2.9xy\hat x + 7.3x\hat y$  from the origin to the point at x = 2.3 and y = 3.8}
- a) 4.48E+01
- b) 4.80E+01
+ c) 5.13E+01
- d) 5.49E+01
- e) 5.88E+01
===4===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 1.3xy\hat x + 6.4x\hat y$  from the origin to the point at x = 2.2 and y = 3.6}
- a) 3.07E+01
+ b) 3.29E+01
- c) 3.52E+01
- d) 3.77E+01
- e) 4.03E+01
===5===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 2.6xy\hat x + 8.6x\hat y$  from the origin to the point at x = 2.9 and y = 3.7}
+ a) 7.31E+01
- b) 7.82E+01
- c) 8.37E+01
- d) 8.96E+01
- e) 9.58E+01
===6===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 4xy\hat x + 9.8x\hat y$  from the origin to the point at x = 2.6 and y = 3.9}
- a) 7.93E+01
+ b) 8.48E+01
- c) 9.08E+01
- d) 9.71E+01
- e) 1.04E+02
===7===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 3.8xy\hat x + 5.1x\hat y$  from the origin to the point at x = 2.5 and y = 3.2}
- a) 4.27E+01
+ b) 4.57E+01
- c) 4.89E+01
- d) 5.24E+01
- e) 5.60E+01
===8===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 1.6xy\hat x + 8x\hat y$  from the origin to the point at x = 2.6 and y = 3.4}
+ a) 4.76E+01
- b) 5.10E+01
- c) 5.45E+01
- d) 5.83E+01
- e) 6.24E+01
===9===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 1.2xy\hat x + 5.3x\hat y$  from the origin to the point at x = 2.1 and y = 3.1}
- a) 1.73E+01
- b) 1.85E+01
- c) 1.98E+01
- d) 2.12E+01
+ e) 2.27E+01
===10===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 3.3xy\hat x + 8.7x\hat y$  from the origin to the point at x = 2.1 and y = 3.2}
- a) 4.18E+01
+ b) 4.48E+01
- c) 4.79E+01
- d) 5.12E+01
- e) 5.48E+01
===11===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 3.8xy\hat x + 9.8x\hat y$  from the origin to the point at x = 2.9 and y = 3.4}
- a) 7.90E+01
+ b) 8.45E+01
- c) 9.05E+01
- d) 9.68E+01
- e) 1.04E+02
===12===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 1.6xy\hat x + 8.7x\hat y$  from the origin to the point at x = 2.7 and y = 3.2}
- a) 4.37E+01
- b) 4.68E+01
+ c) 5.00E+01
- d) 5.35E+01
- e) 5.73E+01
===13===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 1.2xy\hat x + 8.3x\hat y$  from the origin to the point at x = 2.8 and y = 3.8}
- a) 4.58E+01
- b) 4.90E+01
- c) 5.24E+01
+ d) 5.61E+01
- e) 6.00E+01
===14===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 2.4xy\hat x + 6.8x\hat y$  from the origin to the point at x = 2.1 and y = 3.8}
+ a) 4.05E+01
- b) 4.34E+01
- c) 4.64E+01
- d) 4.97E+01
- e) 5.31E+01
===15===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 1.1xy\hat x + 6.4x\hat y$  from the origin to the point at x = 2.9 and y = 3.7}
- a) 4.28E+01
+ b) 4.57E+01
- c) 4.89E+01
- d) 5.24E+01
- e) 5.60E+01
===16===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 3.7xy\hat x + 8.4x\hat y$  from the origin to the point at x = 2.6 and y = 3.4}
- a) 5.00E+01
- b) 5.34E+01
- c) 5.72E+01
- d) 6.12E+01
+ e) 6.55E+01
===17===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 3.6xy\hat x + 5.1x\hat y$  from the origin to the point at x = 2.2 and y = 3.5}
- a) 3.49E+01
- b) 3.73E+01
+ c) 4.00E+01
- d) 4.28E+01
- e) 4.58E+01
===18===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 2xy\hat x + 7.2x\hat y$  from the origin to the point at x = 2.4 and y = 3.2}
- a) 3.05E+01
- b) 3.26E+01
- c) 3.49E+01
- d) 3.73E+01
+ e) 3.99E+01
===19===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 2.2xy\hat x + 9.2x\hat y$  from the origin to the point at x = 2.1 and y = 3.4}
+ a) 4.38E+01
- b) 4.69E+01
- c) 5.02E+01
- d) 5.37E+01
- e) 5.75E+01
===20===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 2xy\hat x + 9.7x\hat y$  from the origin to the point at x = 2.8 and y = 3.2}
- a) 5.26E+01
- b) 5.62E+01
+ c) 6.02E+01
- d) 6.44E+01
- e) 6.89E+01
===21===
{<!--a07energy_lineIntegral_3-->Integrate the line integral of $\vec F = 2xy\hat x + 9.5x\hat y$  from the origin to the point at x = 2.1 and y = 3.8}
+ a) 4.91E+01
- b) 5.25E+01
- c) 5.62E+01
- d) 6.01E+01
- e) 6.43E+01


## a07energy_lineIntegral_4_v1

Integrate the function, ${\displaystyle {\vec {F}}=-x^{2}y^{2}{\hat {x}}+x^{2}y^{3}{\hat {y}}}$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule

 a) 4.45E-01 b) 4.76E-01 c) 5.10E-01 d) 5.45E-01 e) 5.83E-01

copies
===2===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^2y^3\hat x + x^2y^4\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 4.66E-01
- b) 4.98E-01
+ c) 5.33E-01
- d) 5.71E-01
- e) 6.11E-01
===3===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^3y^5\hat x + x^2y^3\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.81E-01
- b) 4.08E-01
- c) 4.37E-01
- d) 4.67E-01
+ e) 5.00E-01
===4===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^5y^2\hat x + x^5y^3\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.64E-01
- b) 3.89E-01
+ c) 4.17E-01
- d) 4.46E-01
- e) 4.77E-01
===5===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^4y^4\hat x + x^5y^4\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.27E-01
- b) 3.49E-01
- c) 3.74E-01
+ d) 4.00E-01
- e) 4.28E-01
===6===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^3y^5\hat x + x^5y^2\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 4.76E-01
- b) 5.10E-01
- c) 5.45E-01
+ d) 5.83E-01
- e) 6.24E-01
===7===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^5y^4\hat x + x^5y^4\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
+ a) 3.67E-01
- b) 3.92E-01
- c) 4.20E-01
- d) 4.49E-01
- e) 4.81E-01
===8===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^4y^5\hat x + x^3y^3\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 4.21E-01
+ b) 4.50E-01
- c) 4.82E-01
- d) 5.15E-01
- e) 5.51E-01
===9===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^5y^3\hat x + x^5y^4\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.43E-01
+ b) 3.67E-01
- c) 3.92E-01
- d) 4.20E-01
- e) 4.49E-01
===10===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^2y^2\hat x + x^4y^3\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 5.10E-01
- b) 5.45E-01
+ c) 5.83E-01
- d) 6.24E-01
- e) 6.68E-01
===11===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^2y^5\hat x + x^2y^4\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
+ a) 5.33E-01
- b) 5.71E-01
- c) 6.11E-01
- d) 6.53E-01
- e) 6.99E-01
===12===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^3y^4\hat x + x^4y^4\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.43E-01
- b) 3.67E-01
- c) 3.93E-01
- d) 4.21E-01
+ e) 4.50E-01
===13===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^2y^4\hat x + x^4y^5\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 4.08E-01
- b) 4.37E-01
- c) 4.67E-01
+ d) 5.00E-01
- e) 5.35E-01
===14===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^5y^2\hat x + x^2y^4\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.43E-01
+ b) 3.67E-01
- c) 3.92E-01
- d) 4.20E-01
- e) 4.49E-01
===15===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^4y^2\hat x + x^4y^5\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
+ a) 3.67E-01
- b) 3.92E-01
- c) 4.20E-01
- d) 4.49E-01
- e) 4.81E-01
===16===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^3y^2\hat x + x^2y^4\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.43E-01
- b) 3.67E-01
- c) 3.93E-01
- d) 4.21E-01
+ e) 4.50E-01
===17===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^4y^2\hat x + x^3y^4\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.74E-01
+ b) 4.00E-01
- c) 4.28E-01
- d) 4.58E-01
- e) 4.90E-01
===18===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^2y^4\hat x + x^4y^3\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 5.10E-01
- b) 5.45E-01
+ c) 5.83E-01
- d) 6.24E-01
- e) 6.68E-01
===19===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^4y^2\hat x + x^2y^3\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
+ a) 4.50E-01
- b) 4.82E-01
- c) 5.15E-01
- d) 5.51E-01
- e) 5.90E-01
===20===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^5y^5\hat x + x^5y^5\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
- a) 3.12E-01
+ b) 3.33E-01
- c) 3.57E-01
- d) 3.82E-01
- e) 4.08E-01
===21===
{<!--a07energy_lineIntegral_4-->Integrate the function, $\vec F = -x^3y^2\hat x + x^5y^3\hat y$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule}
+ a) 5.00E-01
- b) 5.35E-01
- c) 5.72E-01
- d) 6.13E-01
- e) 6.55E-01