integral from-2 to 0 of (3xsqrt(4-x^2))

Lösung

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

- 8

Schritte zur Lösung

\int_{- 2}^{0} 3 x 4 - x^{2} d x

Entferne die Konstante:

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

= 3 \cdot \int_{- 2}^{0} x 4 - x^{2} d x

Wende U-Substitution an

= 3 \cdot \int_{0}^{4} - \frac{u}{2} d u

Entferne die Konstante:

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

= 3 (- \frac{1}{2} \cdot \int_{0}^{4} u d u)

Wende die Potenzregel an

= 3 (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{4})

Vereinfache

3 (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{4}) : - \frac{3}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{4}

= - \frac{3}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{4}

Berechne die Grenzen:

\frac{16}{3}

= - \frac{3}{2} \cdot \frac{16}{3}

Vereinfache

= - 8

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

\int_{- 2}^{0} - c x d x

\int_{0}^{π} e^{3 x} \cdot sin (x) d x

\int_{- 1}^{1} (3 x^{2} + x + 1) d x

\int_{0}^{2} 300 e^{(3 x - 4)} d x