What is the integral from-6 to 6 of pi(36-x^2) ?

The integral from-6 to 6 of pi(36-x^2) is 288pi

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integral from-6 to 6 of pi(36-x^2)

\int_{- 6}^{6} π (36 - x^{2}) d x

288 π

Decimal Notation

904.77868 \dots

Solution steps

\int_{- 6}^{6} π (36 - 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_{- 6}^{6} 36 - 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_{- 6}^{6} 36 d x - \int_{- 6}^{6} x^{2} d x)

\int_{- 6}^{6} 36 d x = 432

\int_{- 6}^{6} x^{2} d x = 144

= π (432 - 144)

Simplify

= 288 π

\frac{d y}{d x} + \frac{1}{x} y = 6 x^{2}

f (x) = \frac{1}{( 1 + x ^{2} )}, at x = - 1

x \to - 10 lim ((+) f (x))

\frac{\partial}{\partial y} (e^{13 x y})

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

What is the integral from-6 to 6 of pi(36-x^2) ?
The integral from-6 to 6 of pi(36-x^2) is 288pi