What is the integral from 0 to 1 of xcos(2pix) ?

The integral from 0 to 1 of xcos(2pix) is 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of xcos(2pix)

\int_{0}^{1} x cos (2 π x) d x

0

Solution steps

\int_{0}^{1} x cos (2 π x) d x

Apply Integration By Parts

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

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

\int \frac{1}{2 π} sin (2 π x) d x = - \frac{1}{4 π ^{2}} cos (2 π x)

= [\frac{1}{2 π} x sin (2 π x) - (- \frac{1}{4 π ^{2}} cos (2 π x))]_{0}^{1}

Simplify

= [\frac{1}{2 π} x sin (2 π x) + \frac{1}{4 π ^{2}} cos (2 π x)]_{0}^{1}

Compute the boundaries:

0

= 0

- 2 x + 5

\int x sec^{2} (6 x) d x

\int (6 x^{5} - \frac{5}{x ^{5}}) d x

\frac{d y}{d x} = \frac{e ^{x}}{9 + e ^{x}}

(1 + x) y^{^{'}} = (x + 2) (y - 1)

What is the integral from 0 to 1 of xcos(2pix) ?
The integral from 0 to 1 of xcos(2pix) is 0