What is the integral from 0 to 3 of pi(9-x^2) ?

The integral from 0 to 3 of pi(9-x^2) is 18pi

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integral from 0 to 3 of pi(9-x^2)

\int_{0}^{3} π (9 - x^{2}) d x

18 π

Decimal Notation

56.54866 \dots

Solution steps

\int_{0}^{3} π (9 - x^{2}) d x

Take the constant out:

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

= π \cdot \int_{0}^{3} 9 - x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= π (\int_{0}^{3} 9 d x - \int_{0}^{3} x^{2} d x)

\int_{0}^{3} 9 d x = 27

\int_{0}^{3} x^{2} d x = 9

= π (27 - 9)

Simplify

= 18 π

\int_{0}^{x} 3 e^{- t^{2}} d t

\frac{d}{d x} (\frac{3 + sinh ( x )}{1 + coth ^{2} ( x )})

\frac{d}{d x} (arctan (- 5 x))

\frac{\partial}{\partial y} (2 x^{2} - x y - 5 x + 1)

\frac{d y}{d x} + y = y x e^{x + 2}

What is the integral from 0 to 3 of pi(9-x^2) ?
The integral from 0 to 3 of pi(9-x^2) is 18pi