What is the integral from 0 to pi of cos^3(θ)sin(θ) ?

The integral from 0 to pi of cos^3(θ)sin(θ) is 0

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integral from 0 to pi of cos^3(θ)sin(θ)

\int_{0}^{π} cos^{3} (θ) sin (θ) d θ

0

Solution steps

\int_{0}^{π} cos^{3} (θ) sin (θ) d θ

Apply u-substitution

: \int_{1}^{- 1} - u^{3} d u

= \int_{1}^{- 1} - u^{3} d u

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

= - \int_{- 1}^{1} - u^{3} d u

Take the constant out:

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

= - (- \int_{- 1}^{1} u^{3} d u)

Apply the Power Rule

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

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

Simplify

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

Compute the boundaries:

0

= 0

\int_{0}^{1} (x - \frac{3}{4})^{2} 3 x^{2} d x

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

\int_{0}^{0.3} x^{2} d x

\int_{0}^{6} \frac{36 x - x ^{3}}{144} d x

\int_{0}^{3} 10 x - 2 x^{3} d x

What is the integral from 0 to pi of cos^3(θ)sin(θ) ?
The integral from 0 to pi of cos^3(θ)sin(θ) is 0