integral from 0 to 3 of 4pi((x^3)/3)

Lösung

\int_{0}^{3} 4 π (\frac{x ^{3}}{3}) d x

27 π

Dezimale

84.82300 \dots

Schritte zur Lösung

\int_{0}^{3} 4 π \frac{x ^{3}}{3} d x

Entferne die Konstante:

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

= 4 π \frac{1}{3} \cdot \int_{0}^{3} x^{3} d x

4 π \frac{1}{3} = \frac{4 π}{3}

= \frac{4 π}{3} \cdot \int_{0}^{3} x^{3} d x

Wende die Potenzregel an

= \frac{4 π}{3} [\frac{x ^{4}}{4}]_{0}^{3}

Berechne die Grenzen:

\frac{81}{4}

= \frac{4 π}{3} \cdot \frac{81}{4}

Vereinfache

= 27 π

d er i v a t i v e 1 + 10 t

t an g e n t f (x) = \frac{x ^{3}}{4}, (- 6, - 54)

\frac{\partial}{\partial x} (sin (3 x) cos (2 y))

\int (sin (x))^{\frac{1}{3}} cos (x) d x

\int_{6}^{13} ln (x - 6) d x