What is the integral from-1 to 1 of xsin(pix) ?

The integral from-1 to 1 of xsin(pix) is 2/pi

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-1 to 1 of xsin(pix)

\int_{- 1}^{1} x sin (π x) d x

\frac{2}{π}

Decimal

0.63661 \dots

Solution steps

\int_{- 1}^{1} x sin (π x) d x

Apply Integration By Parts

= [- \frac{1}{π} x cos (π x) - \int - \frac{1}{π} cos (π x) d x]_{- 1}^{1}

\int - \frac{1}{π} cos (π x) d x = - \frac{1}{π ^{2}} sin (π x)

= [- \frac{1}{π} x cos (π x) - (- \frac{1}{π ^{2}} sin (π x))]_{- 1}^{1}

Simplify

= [- \frac{1}{π} x cos (π x) + \frac{1}{π ^{2}} sin (π x)]_{- 1}^{1}

Compute the boundaries:

\frac{2}{π}

= \frac{2}{π}

What is the integral from-1 to 1 of xsin(pix) ?
The integral from-1 to 1 of xsin(pix) is 2/pi