What is the integral from 0 to pi/2 of x*cos(x) ?

The integral from 0 to pi/2 of x*cos(x) is pi/2-1

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integral from 0 to pi/2 of x*cos(x)

\int_{0}^{\frac{π}{2}} x \cdot cos (x) d x

\frac{π}{2} - 1

Decimal Notation

0.57079 \dots

Solution steps

\int_{0}^{\frac{π}{2}} x cos (x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

\frac{π}{2} - 1

= \frac{π}{2} - 1

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

\int_{- 2}^{- 1} 2 x^{- 4} d x

\int_{0}^{1} 2 z x e^{- x^{2}} d x

\int_{0}^{zy} z d z

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

What is the integral from 0 to pi/2 of x*cos(x) ?
The integral from 0 to pi/2 of x*cos(x) is pi/2-1