What is the integral from 0 to pi of x*sin(x) ?

The integral from 0 to pi of x*sin(x) is pi

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integral from 0 to pi of x*sin(x)

\int_{0}^{π} x \cdot sin (x) d x

π

Decimal

3.14159 \dots

Solution steps

\int_{0}^{π} x sin (x) d x

Apply Integration By Parts

= [- x cos (x) - \int - cos (x) d x]_{0}^{π}

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

= [- x cos (x) - (- sin (x))]_{0}^{π}

Simplify

= [- x cos (x) + sin (x)]_{0}^{π}

Compute the boundaries:

π

= π

What is the integral from 0 to pi of x*sin(x) ?
The integral from 0 to pi of x*sin(x) is pi