What is the integral from (-pi)/2 to pi/2 of xcos(x) ?

The integral from (-pi)/2 to pi/2 of xcos(x) is 0

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integral from (-pi)/2 to pi/2 of xcos(x)

\int_{\frac{- π}{2}}^{\frac{π}{2}} x cos (x) d x

0

Solution steps

\int_{\frac{- π}{2}}^{\frac{π}{2}} x cos (x) d x

Apply Integration By Parts

: [x sin (x) - \int sin (x) d x]_{- \frac{π}{2}}^{\frac{π}{2}}

= [x sin (x) - \int sin (x) d x]_{- \frac{π}{2}}^{\frac{π}{2}}

\int sin (x) d x = - cos (x)

= [x sin (x) - (- cos (x))]_{- \frac{π}{2}}^{\frac{π}{2}}

Simplify

= [x sin (x) + cos (x)]_{- \frac{π}{2}}^{\frac{π}{2}}

Compute the boundaries:

0

= 0

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\int_{0}^{5} 1 + 2 x^{3} d x

\int_{0}^{3} 2 x (x - 7) d x

What is the integral from (-pi)/2 to pi/2 of xcos(x) ?
The integral from (-pi)/2 to pi/2 of xcos(x) is 0