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

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

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

\int_{0}^{π} cos^{4} (x) sin (x) d x

\frac{2}{5}

Decimal Notation

0.4

Solution steps

\int_{0}^{π} cos^{4} (x) sin (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}

\frac{\partial}{\partial y} (x + 2 y - 6)

\int_{- 8}^{8} 64 - x^{2} d x

\int 9 x e^{x^{2}} d x

h (t - 2 π) sin (t - 2 π)

\frac{d}{d x} (x^{4} y)

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