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

The integral from 0 to pi of sin(x)cos^4(x) is 2/5

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

\int_{0}^{π} sin (x) cos^{4} (x) d x

\frac{2}{5}

Decimal

0.4

Solution steps

\int_{0}^{π} sin (x) cos^{4} (x) d x

Apply u-substitution

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

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

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

= - \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

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

Apply the Power Rule

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

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

Simplify

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

Compute the boundaries:

\frac{2}{5}

= \frac{2}{5}

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What is the integral from 0 to pi of sin(x)cos^4(x) ?
The integral from 0 to pi of sin(x)cos^4(x) is 2/5