What is the integral from-pi/2 to pi/2 of xsin(x) ?

The integral from-pi/2 to pi/2 of xsin(x) is 2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-pi/2 to pi/2 of xsin(x)

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

2

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

2

= 2

\int_{0}^{l o g_{3} (7)} 3^{x} d x

\int_{2}^{5} 3^{2 x} d x

\int_{2}^{3} (4 - x^{2}) d x

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

\int_{- 3}^{4} - x + 1 d x

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