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Beliebt Rechnen >

integral from 0 to 2 of pi(3x^2)^2

Lösung

\int_{0}^{2} π (3 x^{2})^{2} d x

Lösung

\frac{288 π}{5}

+1

Dezimale

180.95573 \dots

Schritte zur Lösung

\int_{0}^{2} π (3 x^{2})^{2} d x

Entferne die Konstante:

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

= π \cdot \int_{0}^{2} (3 x^{2})^{2} d x

Vereinfache

(3 x^{2})^{2} : 9 x^{4}

= π \cdot \int_{0}^{2} 9 x^{4} d x

Entferne die Konstante:

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

= π 9 \cdot \int_{0}^{2} x^{4} d x

Wende die Potenzregel an

= π 9 [\frac{x ^{5}}{5}]_{0}^{2}

Berechne die Grenzen:

\frac{32}{5}

= π 9 \cdot \frac{32}{5}

Vereinfache

= \frac{288 π}{5}

Graph

Beliebte Beispiele

(\partial)/(\partial x)(4x^2+3y^4)

\frac{\partial}{\partial x} (4 x^{2} + 3 y^{4})

limit as x approaches 1-of 1/x-1

x \to 1 - lim (\frac{1}{x} - 1)

y^{''}+9y=3sec(3t)

y^{^{''}} + 9 y = 3 sec (3 t)

f(x)=cos(x^2)*2x

f (x) = cos (x^{2}) \cdot 2 x

fläche y=x+1,y=9-x^2,x=-1,x=2

a re a y = x + 1, y = 9 - x^{2}, x = - 1, x = 2