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

Only version A of this testbank has been tested.

## pe07lineIntegral-A

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

 a) 8.98E+04 b) 1.13E+05 c) 1.42E+05 d) 1.79E+05 e) 2.25E+05

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

 a) 1.95E+07 b) 2.36E+07 c) 2.86E+07 d) 3.47E+07 e) 4.20E+07

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

 a) 2.97E+01 b) 3.74E+01 c) 4.71E+01 d) 5.93E+01 e) 7.46E+01

4 Integrate the function, ${\vec {F}}=-x^{2}y^{2}{\hat {x}}+x^{2}y^{3}{\hat {y}}$ , 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) 5.83E-01 b) 7.07E-01 c) 8.56E-01 d) 1.04E+00 e) 1.26E+00

## pe07lineIntegral B

1 Integrate the line integral of, ${\vec {F}}=7.8xy{\hat {x}}+9.6y^{3}{\hat {y}}$ , along the y axis from y = 6 to y = 16

 a) 9.73E+04 b) 1.22E+05 c) 1.54E+05 d) 1.94E+05 e) 2.44E+05

2 Integrate the function, ${\vec {F}}=r^{8}\theta ^{9}{\hat {r}}+r^{9}\theta ^{3}{\hat {\theta }}$ , along the first quadrant of a circle of radius 9

 a) 2.46E+09 b) 2.98E+09 c) 3.62E+09 d) 4.38E+09 e) 5.31E+09

3 Integrate the line integral of ${\vec {F}}=2.9xy{\hat {x}}+9.9x{\hat {y}}$ from the origin to the point at x = 2.5 and y = 3.5

 a) 3.23E+01 b) 4.07E+01 c) 5.12E+01 d) 6.45E+01 e) 8.11E+01

4 Integrate the function, ${\vec {F}}=-x^{5}y^{2}{\hat {x}}+x^{3}y^{5}{\hat {y}}$ , 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) 2.27E-01 b) 2.75E-01 c) 3.33E-01 d) 4.04E-01 e) 4.89E-01

## pe07lineIntegral C

1 Integrate the line integral of, ${\vec {F}}=6.3xy{\hat {x}}+8.3y^{3}{\hat {y}}$ , along the y axis from y = 3 to y = 16

 a) 1.08E+05 b) 1.36E+05 c) 1.71E+05 d) 2.15E+05 e) 2.71E+05

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

 a) 6.69E+09 b) 8.11E+09 c) 9.82E+09 d) 1.19E+10 e) 1.44E+10

3 Integrate the line integral of ${\vec {F}}=2.9xy{\hat {x}}+9.6x{\hat {y}}$ from the origin to the point at x = 2.6 and y = 3.1

 a) 2.95E+01 b) 3.72E+01 c) 4.68E+01 d) 5.89E+01 e) 7.42E+01

4 Integrate the function, ${\vec {F}}=-x^{2}y^{5}{\hat {x}}+x^{3}y^{5}{\hat {y}}$ , 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) 5.00E-01 b) 6.06E-01 c) 7.34E-01 d) 8.89E-01 e) 1.08E+00