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

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

Popular >

integral from 0 to pi/2 of (xcos(x))

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

\frac{π}{2} - 1

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

\int_{3}^{7} 6 - 2 x d x

\int_{4}^{0} x^{\frac{1}{2}} d x

\int_{0}^{1} (4 x - 3) d x

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

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