What is the integral from 0 to pi/4 of xcos(x) ?

The integral from 0 to pi/4 of xcos(x) is pi/(4sqrt(2))+1/(sqrt(2))-1

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integral from 0 to pi/4 of xcos(x)

\int_{0}^{\frac{π}{4}} x cos (x) d x

\frac{π}{4 2} + \frac{1}{2} - 1

Decimal

0.26246 \dots

Solution steps

\int_{0}^{\frac{π}{4}} x cos (x) d x

Apply Integration By Parts

: [x sin (x) - \int sin (x) d x]_{0}^{\frac{π}{4}}

= [x sin (x) - \int sin (x) d x]_{0}^{\frac{π}{4}}

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

= [x sin (x) - (- cos (x))]_{0}^{\frac{π}{4}}

Simplify

= [x sin (x) + cos (x)]_{0}^{\frac{π}{4}}

Compute the boundaries:

\frac{π}{4 2} + \frac{1}{2} - 1

= \frac{π}{4 2} + \frac{1}{2} - 1

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What is the integral from 0 to pi/4 of xcos(x) ?
The integral from 0 to pi/4 of xcos(x) is pi/(4sqrt(2))+1/(sqrt(2))-1