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

The integral from 0 to pi of 4cos^4(x)sin(x) is 8/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to pi of 4cos^4(x)sin(x)

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

\frac{8}{5}

Decimal

1.6

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

= 4 \cdot \int_{1}^{- 1} - u^{4} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= 4 (- \int_{- 1}^{1} - u^{4} d u)

Take the constant out:

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

= 4 (- (- \int_{- 1}^{1} u^{4} d u))

Apply the Power Rule

= 4 (- (- [\frac{u ^{5}}{5}]_{- 1}^{1}))

Simplify

= 4 [\frac{u ^{5}}{5}]_{- 1}^{1}

Compute the boundaries:

\frac{2}{5}

= 4 \cdot \frac{2}{5}

Simplify

= \frac{8}{5}

What is the integral from 0 to pi of 4cos^4(x)sin(x) ?
The integral from 0 to pi of 4cos^4(x)sin(x) is 8/5