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

The integral from-3 to 3 of pi(9-x^2)^2 is pi 1296/5

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

\int_{- 3}^{3} π (9 - x^{2})^{2} d x

π \frac{1296}{5}

Decimal

814.30081 \dots

Solution steps

\int_{- 3}^{3} π (9 - x^{2})^{2} d x

Take the constant out:

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

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

Expand

(9 - x^{2})^{2} : 81 - 18 x^{2} + x^{4}

= π \cdot \int_{- 3}^{3} 81 - 18 x^{2} + x^{4} 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_{- 3}^{3} 81 d x - \int_{- 3}^{3} 18 x^{2} d x + \int_{- 3}^{3} x^{4} d x)

\int_{- 3}^{3} 81 d x = 486

\int_{- 3}^{3} 18 x^{2} d x = 324

\int_{- 3}^{3} x^{4} d x = \frac{486}{5}

= π (486 - 324 + \frac{486}{5})

Simplify

π (486 - 324 + \frac{486}{5}) : π \frac{1296}{5}

= π \frac{1296}{5}

x \to 5 lim ((4 - x)^{\frac{3}{2}})

\int \frac{8 x ^{3}}{3} d x

(2 x - 1)^{2} ln (2 x - 1), at x = 0

\frac{d}{d x} (3 x^{2} cos (x^{3}))

\frac{d y}{d t} + 3 y = cos (2 t)

What is the integral from-3 to 3 of pi(9-x^2)^2 ?
The integral from-3 to 3 of pi(9-x^2)^2 is pi 1296/5