integral from 0 to pi of 3cos^2(x)sin(x)

Lösung

\int_{0}^{π} 3 cos^{2} (x) sin (x) d x

2

Schritte zur Lösung

\int_{0}^{π} 3 cos^{2} (x) sin (x) d x

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{π} cos^{2} (x) sin (x) d x

Wende U-Substitution an

= 3 \cdot \int_{1}^{- 1} - u^{2} d u

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

= 3 (- \int_{- 1}^{1} - u^{2} d u)

Entferne die Konstante:

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

= 3 (- (- \int_{- 1}^{1} u^{2} d u))

Wende die Potenzregel an

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

Vereinfache

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

Berechne die Grenzen:

\frac{2}{3}

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

Vereinfache

= 2

x \to 2 lim (8 - x)

\int 4^{x} sin (4^{x}) d x

x \to 0 + lim (sin (x) ln (4 x))

\int t cos (n t) d t

k \to \infty lim (\frac{k ^{\frac{1}{k}}}{ln ( k )})