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

Lösung

\int_{0}^{π} cos^{3} (θ) sin (θ) d θ

0

Schritte zur Lösung

\int_{0}^{π} cos^{3} (θ) sin (θ) d θ

Wende U-Substitution an

= \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

Entferne die Konstante:

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

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

Wende die Potenzregel an

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

Vereinfache

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

Berechne die Grenzen:

0

= 0

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