What is the integral from 0 to pi of tsin(t) ?

The integral from 0 to pi of tsin(t) is pi

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integral from 0 to pi of tsin(t)

\int_{0}^{π} t sin (t) d t

π

Solution steps

\int_{0}^{π} t sin (t) d t

Apply Integration By Parts

: [- t cos (t) - \int - cos (t) d t]_{0}^{π}

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

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

= [- t cos (t) - (- sin (t))]_{0}^{π}

Simplify

= [- t cos (t) + sin (t)]_{0}^{π}

Compute the boundaries:

π

= π

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What is the integral from 0 to pi of tsin(t) ?
The integral from 0 to pi of tsin(t) is pi