What is the integral from 0 to 1 of sin^4(x)*cos(x) ?

The integral from 0 to 1 of sin^4(x)*cos(x) is (sin^5(1))/5

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 sin^4(x)*cos(x)

\int_{0}^{1} sin^{4} (x) \cdot cos (x) d x

\frac{sin ^{5} ( 1 )}{5}

Decimal

0.08437 \dots

Solution steps

\int_{0}^{1} sin^{4} (x) cos (x) d x

Apply u-substitution

: \int_{0}^{s i n (1)} u^{4} d u

= \int_{0}^{s i n (1)} u^{4} d u

Apply the Power Rule

: [\frac{u ^{5}}{5}]_{0}^{s i n (1)}

= [\frac{u ^{5}}{5}]_{0}^{s i n (1)}

Compute the boundaries:

\frac{sin ^{5} ( 1 )}{5}

= \frac{sin ^{5} ( 1 )}{5}

\int_{- π}^{π} \frac{sin ( x )}{x} d x

\int_{- 3}^{- 2} \frac{x}{( x ^{2} + 6 ) ^{2}} d x

\int_{- 1}^{4} 3 x^{2} + 8 x d x

\int_{2}^{x} \frac{1}{1 + x ^{4}} d x

\int_{0}^{1} r 1 + 4 r^{2} d r

What is the integral from 0 to 1 of sin^4(x)*cos(x) ?
The integral from 0 to 1 of sin^4(x)*cos(x) is (sin^5(1))/5