What is the integral from 0 to pi of 3xsin(x) ?

The integral from 0 to pi of 3xsin(x) is 3pi

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 3xsin(x)

\int_{0}^{π} 3 x sin (x) d x

3 π

Decimal

9.42477 \dots

Solution steps

\int_{0}^{π} 3 x sin (x) d x

Take the constant out:

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

= 3 \cdot \int_{0}^{π} x sin (x) d x

Apply Integration By Parts

: [- x cos (x) - \int - cos (x) d x]_{0}^{π}

= 3 [- x cos (x) - \int - cos (x) d x]_{0}^{π}

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

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

Simplify

= 3 [- x cos (x) + sin (x)]_{0}^{π}

Compute the boundaries:

π

= 3 π

\frac{d}{d x} (3 sec (6 x))

\frac{10}{s ( s + 2 ) ^{2}}

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

f (x) = 3 x^{2} - x

f (x) = 18

What is the integral from 0 to pi of 3xsin(x) ?
The integral from 0 to pi of 3xsin(x) is 3pi