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

The integral from 0 to pi/2 of x^2cos(x) is (pi^2)/4-2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{π ^{2}}{4} - 2

Decimal

0.46740 \dots

Solution steps

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

Apply Integration By Parts

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

\int 2 x sin (x) d x = 2 (- x cos (x) + sin (x))

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

Compute the boundaries:

\frac{π ^{2}}{4} - 2

= \frac{π ^{2}}{4} - 2

What is the integral from 0 to pi/2 of x^2cos(x) ?
The integral from 0 to pi/2 of x^2cos(x) is (pi^2)/4-2