integral from-4 to 0 of x^3sqrt(256-x^4)

Lösung

\int_{- 4}^{0} x^{3} 256 - x^{4} d x

- \frac{2048}{3}

Dezimale

- 682.66666 \dots

Schritte zur Lösung

\int_{- 4}^{0} x^{3} 256 - x^{4} d x

Wende U-Substitution an

= \int_{0}^{256} - \frac{u}{4} d u

Entferne die Konstante:

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

= - \frac{1}{4} \cdot \int_{0}^{256} u d u

Wende die Potenzregel an

= - \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{256}

Berechne die Grenzen:

\frac{8192}{3}

= - \frac{1}{4} \cdot \frac{8192}{3}

Vereinfache

= - \frac{2048}{3}

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

\int_{x}^{1} y d y

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

\int_{3}^{9} (\frac{1}{x ^{2}}) d x

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