What is the integral from 0 to pi of 10tsin(3t) ?

The integral from 0 to pi of 10tsin(3t) is (10pi)/3

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 10tsin(3t)

\int_{0}^{π} 10 t sin (3 t) d t

\frac{10 π}{3}

Decimal Notation

10.47197 \dots

Solution steps

\int_{0}^{π} 10 t sin (3 t) d t

Take the constant out:

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

= 10 \cdot \int_{0}^{π} t sin (3 t) d t

Apply Integration By Parts

: [\frac{1}{3} (- t cos (3 t) - 3 \cdot \int - \frac{1}{3} cos (3 t) d t)]_{0}^{π}

= 10 [\frac{1}{3} (- t cos (3 t) - 3 \cdot \int - \frac{1}{3} cos (3 t) d t)]_{0}^{π}

\int - \frac{1}{3} cos (3 t) d t = - \frac{1}{9} sin (3 t)

= 10 [\frac{1}{3} (- t cos (3 t) - 3 (- \frac{1}{9} sin (3 t)))]_{0}^{π}

Simplify

10 [\frac{1}{3} (- t cos (3 t) - 3 (- \frac{1}{9} sin (3 t)))]_{0}^{π} : 10 [\frac{1}{3} (- t cos (3 t) + \frac{1}{3} sin (3 t))]_{0}^{π}

= 10 [\frac{1}{3} (- t cos (3 t) + \frac{1}{3} sin (3 t))]_{0}^{π}

Compute the boundaries:

\frac{π}{3}

= 10 \cdot \frac{π}{3}

Simplify

= \frac{10 π}{3}

f (x) = x^{4} + 9 x^{2} - x, (1, 9)

x \to \infty lim (\frac{x \cdot ( x + 1 ) ^{x + 1}}{( x + 1 ) ^{x + 2}})

\frac{1}{( 8 ^{2} + 1 ) + ( 8 ^{2} + 4 )}

\int 2 e^{- 0.4 x} d x

\frac{d}{d x} (144 + x^{2})

What is the integral from 0 to pi of 10tsin(3t) ?
The integral from 0 to pi of 10tsin(3t) is (10pi)/3