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 Notation

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}}

= [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

\int_{0}^{\frac{π}{6}} 9 sin^{2} (x) d x

\int_{\frac{π}{2}}^{π} cot (x) d x

\int_{0}^{4} 16 - y^{2} d y

\int_{0}^{\frac{π}{3}} sin (2 x) sin (x) d x

\int_{8}^{15} \frac{1}{( x - 8 ) ^{7}} d x

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