What is the integral from 0 to pi of 7cos^4(x)sin(x) ?

The integral from 0 to pi of 7cos^4(x)sin(x) is 14/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to pi of 7cos^4(x)sin(x)

\int_{0}^{π} 7 cos^{4} (x) sin (x) d x

\frac{14}{5}

Decimal

2.8

Solution steps

\int_{0}^{π} 7 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

= 7 \cdot \int_{0}^{π} cos^{4} (x) sin (x) d x

Apply u-substitution

: \int_{1}^{- 1} - u^{4} d u

= 7 \cdot \int_{1}^{- 1} - u^{4} d u

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

= 7 (- \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

= 7 (- (- \int_{- 1}^{1} u^{4} d u))

Apply the Power Rule

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

= 7 (- (- [\frac{u ^{5}}{5}]_{- 1}^{1}))

Simplify

= 7 [\frac{u ^{5}}{5}]_{- 1}^{1}

Compute the boundaries:

\frac{2}{5}

= 7 \cdot \frac{2}{5}

Simplify

= \frac{14}{5}

\int_{- 8}^{- 4} (x - \frac{24}{x ^{2}}) d x

\int_{0}^{1} 16 x d x

\int_{1}^{4} 3 x + 3 d x

\int_{- 1}^{1} (2 x + ∣ x ∣ + 1)^{2} d x

\int_{3}^{9} \frac{1}{x ( ln ( x ) ) ^{6}} d x

What is the integral from 0 to pi of 7cos^4(x)sin(x) ?
The integral from 0 to pi of 7cos^4(x)sin(x) is 14/5