integral from 0 to 9 of pi(y^{3/2})^2

Lösung

\int_{0}^{9} π (y^{\frac{3}{2}})^{2} d y

\frac{6561 π}{4}

Dezimale

5152.99735 \dots

Schritte zur Lösung

\int_{0}^{9} π (y^{\frac{3}{2}})^{2} d y

Entferne die Konstante:

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

= π \cdot \int_{0}^{9} (y^{\frac{3}{2}})^{2} d y

Vereinfache

(y^{\frac{3}{2}})^{2} : y^{3}

= π \cdot \int_{0}^{9} y^{3} d y

Wende die Potenzregel an

= π [\frac{y ^{4}}{4}]_{0}^{9}

Berechne die Grenzen:

\frac{6561}{4}

= π \frac{6561}{4}

Vereinfache

= \frac{6561 π}{4}

n = 0 \sum \infty \frac{5 ^{n}}{4 ^{n}}

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