What is the integral from 0 to pi of vsin(v) ?

The integral from 0 to pi of vsin(v) is pi

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integral from 0 to pi of vsin(v)

\int_{0}^{π} v sin (v) d v

π

Decimal

3.14159 \dots

Solution steps

\int_{0}^{π} v sin (v) d v

Apply Integration By Parts

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

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

= [- v cos (v) - (- sin (v))]_{0}^{π}

Simplify

= [- v cos (v) + sin (v)]_{0}^{π}

Compute the boundaries:

π

= π

What is the integral from 0 to pi of vsin(v) ?
The integral from 0 to pi of vsin(v) is pi