What is the integral from pi/2 to pi of x*cos(x) ?

The integral from pi/2 to pi of x*cos(x) is -1-pi/2

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integral from pi/2 to pi of x*cos(x)

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

- 1 - \frac{π}{2}

Decimal Notation

- 2.57079 \dots

Solution steps

\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}

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