integral from 0 to b of pix^2

Lösung

\int_{0}^{b} π x^{2} d x

\frac{π b ^{3}}{3}

Schritte zur Lösung

\int_{0}^{b} π x^{2} d x

Entferne die Konstante:

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

= π \cdot \int_{0}^{b} x^{2} d x

Wende die Potenzregel an

= π [\frac{x ^{3}}{3}]_{0}^{b}

Berechne die Grenzen:

\frac{b ^{3}}{3}

= π \frac{b ^{3}}{3}

Vereinfache

= \frac{π b ^{3}}{3}

\int_{0}^{π} 1 + x^{2} d x

\int_{3}^{6} - 5 x + 6 d x

\int_{1}^{7} \frac{1}{5 x} d x

\int_{\frac{π}{6}}^{\frac{π}{3}} sin (θ) d θ

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