What is the integral from 0 to pi of ysin(y) ?

The integral from 0 to pi of ysin(y) is pi

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integral from 0 to pi of ysin(y)

\int_{0}^{π} y sin (y) d y

π

Decimal

3.14159 \dots

Solution steps

\int_{0}^{π} y sin (y) d y

Apply Integration By Parts

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

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

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

= [- y cos (y) - (- sin (y))]_{0}^{π}

Simplify

= [- y cos (y) + sin (y)]_{0}^{π}

Compute the boundaries:

π

= π

\int_{0}^{1} (2 - x) d x

\int_{1}^{5} 2 x + 7 d x

\int_{0}^{18 π} sin (x) d x

\int_{1}^{2} \frac{x - 3}{x ^{3} + x ^{2}} d x

\int_{0}^{t} u d u

What is the integral from 0 to pi of ysin(y) ?
The integral from 0 to pi of ysin(y) is pi