# University of Florida/Egm4313/s12.team11.gooding.k/R7

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##### Scalar Product

${\displaystyle =\int _{a}^{b}f(x)g(x)\ dx\!}$

${\displaystyle =\int _{-2}^{10}x\cos(x)\ dx\!}$

Using integration by parts;

${\displaystyle =[x\sin(x)+\cos(x)]_{-2}^{10}}$

                      ${\displaystyle =-7.68\!}$

##### Magnitude

${\displaystyle \|f\|=^{1/2}=\int _{a}^{b}f^{2}(x)\ dx\!}$

${\displaystyle =\int _{-2}^{10}[\cos(x)]^{2}\ dx\!}$

${\displaystyle =[.5(x+\sin(x)\cos(x)|_{-2}^{10}]^{1/2}}$

                       ${\displaystyle \|f\|=2.457\!}$


${\displaystyle \|g\|=\int _{a}^{b}g^{2}(x)\ dx\!}$

${\displaystyle =\int _{-2}^{10}x^{2}\ dx}$
${\displaystyle =[x^{3}/3]_{-2}^{10}}$

                       ${\displaystyle \|g\|={\frac {1008}{3}}\!}$

##### Angle Between Functions

${\displaystyle cos(\theta )={\frac {}{\|f\|\|g\|}}\!}$

${\displaystyle cos(\theta )={\frac {-7.68}{{\frac {1008}{3}}(2.457)}}}$

                      ${\displaystyle \theta =89.47}$
The two functions are nearly orthogonal.