What is the integral from 0 to pi/2 of ycos(y) ?

The integral from 0 to pi/2 of ycos(y) is pi/2-1

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integral from 0 to pi/2 of ycos(y)

\int_{0}^{\frac{π}{2}} y cos (y) d y

\frac{π}{2} - 1

Decimal

0.57079 \dots

Solution steps

\int_{0}^{\frac{π}{2}} y cos (y) d y

Apply Integration By Parts

= [y sin (y) - \int sin (y) d y]_{0}^{\frac{π}{2}}

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

= [y sin (y) - (- cos (y))]_{0}^{\frac{π}{2}}

Simplify

= [y sin (y) + cos (y)]_{0}^{\frac{π}{2}}

Compute the boundaries:

\frac{π}{2} - 1

= \frac{π}{2} - 1

What is the integral from 0 to pi/2 of ycos(y) ?
The integral from 0 to pi/2 of ycos(y) is pi/2-1