integral from 0 to 9 of pi(2sqrt(y))^2

Lösung

\int_{0}^{9} π (2 y)^{2} d y

π 162

Dezimale

508.93800 \dots

Schritte zur Lösung

\int_{0}^{9} π (2 y)^{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} (2 y)^{2} d y

Wende die partielle Integration an

= π [4 y^{2} - \int 4 y d y]_{0}^{9}

\int 4 y d y = 2 y^{2}

= π [4 y^{2} - 2 y^{2}]_{0}^{9}

Vereinfache

= π [2 y^{2}]_{0}^{9}

Berechne die Grenzen:

162

= π 162

in v erse l a pl a ce 0

\int \frac{cos ( 3 π ) x}{2} d x

3 y^{^{''}} - 4 y^{^{'}} - 15 y = 0, y (0) = - 7, y^{^{'}} (0) = - 2

\frac{d}{d x} ((9 x^{2} - 18 x + 18) e^{x})

\int \frac{1}{sin ^{2} ( x ) cos ^{2} ( x )} d x