What is the integral from 0 to pi of (xcos(2x)) ?

The integral from 0 to pi of (xcos(2x)) 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 pi of (xcos(2x))

\int_{0}^{π} (x cos (2 x)) d x

0

Solution steps

\int_{0}^{π} x cos (2 x) d x

Apply u-substitution

: \int_{0}^{2 π} \frac{u cos ( u )}{4} d u

= \int_{0}^{2 π} \frac{u cos ( u )}{4} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int_{0}^{2 π} u cos (u) d u

Apply Integration By Parts

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

= \frac{1}{4} [u sin (u) - \int sin (u) d u]_{0}^{2 π}

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

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

Simplify

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

Compute the boundaries:

0

= \frac{1}{4} \cdot 0

Simplify

= 0

\frac{d y}{d t} - 0.1 y = - t

\frac{d}{d x} (\frac{9 - x ^{2}}{( 9 + x ^{2} ) ^{2}})

\frac{1}{sin ^{2} ( x )}

\int x^{2} 9 + x d x

\frac{x}{x ^{2} + 1}

What is the integral from 0 to pi of (xcos(2x)) ?
The integral from 0 to pi of (xcos(2x)) is 0