What is the integral from 0 to 3/2 of xcos(pix) ?

The integral from 0 to 3/2 of xcos(pix) is -3/(2pi)-1/(pi^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 3/2 of xcos(pix)

\int_{0}^{\frac{3}{2}} x cos (π x) d x

- \frac{3}{2 π} - \frac{1}{π ^{2}}

Decimal

- 0.57878 \dots

Solution steps

\int_{0}^{\frac{3}{2}} x cos (π x) d x

Apply Integration By Parts

= [\frac{1}{π} (x sin (π x) - π \cdot \int \frac{1}{π} sin (π x) d x)]_{0}^{\frac{3}{2}}

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

= [\frac{1}{π} (x sin (π x) - π (- \frac{1}{π ^{2}} cos (π x)))]_{0}^{\frac{3}{2}}

Simplify

[\frac{1}{π} (x sin (π x) - π (- \frac{1}{π ^{2}} cos (π x)))]_{0}^{\frac{3}{2}} : [\frac{1}{π} (x sin (π x) + \frac{1}{π} cos (π x))]_{0}^{\frac{3}{2}}

= [\frac{1}{π} (x sin (π x) + \frac{1}{π} cos (π x))]_{0}^{\frac{3}{2}}

Compute the boundaries:

- \frac{3}{2 π} - \frac{1}{π ^{2}}

= - \frac{3}{2 π} - \frac{1}{π ^{2}}

What is the integral from 0 to 3/2 of xcos(pix) ?
The integral from 0 to 3/2 of xcos(pix) is -3/(2pi)-1/(pi^2)