integral from 0 to h of pix^2

Lösung

\int_{0}^{h} π x^{2} d x

\frac{π h ^{3}}{3}

Schritte zur Lösung

\int_{0}^{h} 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}^{h} x^{2} d x

Wende die Potenzregel an

= π [\frac{x ^{3}}{3}]_{0}^{h}

Berechne die Grenzen:

\frac{h ^{3}}{3}

= π \frac{h ^{3}}{3}

Vereinfache

= \frac{π h ^{3}}{3}

\int_{1}^{5} x^{2} - 3 x + 1 d x

\int_{0}^{x} (x + y) d y

\int_{3}^{5} (2 x + 1) d x

\int_{- 1}^{3} x^{3} - 3 x^{2} + 5 d x

\int_{- 1}^{1} 3 - x^{2} d x