integral from 0 to pi of-2cos^2(x)sin(x)

Lösung

\int_{0}^{π} - 2 cos^{2} (x) sin (x) d x

- \frac{4}{3}

Dezimale

- 1.33333 \dots

Schritte zur Lösung

\int_{0}^{π} - 2 cos^{2} (x) sin (x) d x

Entferne die Konstante:

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

= - 2 \cdot \int_{0}^{π} cos^{2} (x) sin (x) d x

Wende U-Substitution an

= - 2 \cdot \int_{1}^{- 1} - u^{2} d u

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

= - 2 (- \int_{- 1}^{1} - u^{2} d u)

Entferne die Konstante:

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

= - 2 (- (- \int_{- 1}^{1} u^{2} d u))

Wende die Potenzregel an

= - 2 (- (- [\frac{u ^{3}}{3}]_{- 1}^{1}))

Vereinfache

= - 2 [\frac{u ^{3}}{3}]_{- 1}^{1}

Berechne die Grenzen:

\frac{2}{3}

= - 2 \cdot \frac{2}{3}

Vereinfache

= - \frac{4}{3}

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