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

The integral from pi/2 to pi of (-xcos(x)) is 1+pi/2

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

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

1 + \frac{π}{2}

Decimal

2.57079 \dots

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

- 1 - \frac{π}{2}

= - (- 1 - \frac{π}{2})

Simplify

= 1 + \frac{π}{2}

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What is the integral from pi/2 to pi of (-xcos(x)) ?
The integral from pi/2 to pi of (-xcos(x)) is 1+pi/2