What is the integral from 0 to 6 of pi/4 (36-y^2) ?

The integral from 0 to 6 of pi/4 (36-y^2) is 36pi

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integral from 0 to 6 of pi/4 (36-y^2)

\int_{0}^{6} \frac{π}{4} (36 - y^{2}) d y

36 π

Decimal

113.09733 \dots

Solution steps

\int_{0}^{6} \frac{π}{4} (36 - y^{2}) d y

Take the constant out:

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

= \frac{π}{4} \cdot \int_{0}^{6} 36 - y^{2} d y

Apply the Sum Rule:

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

= \frac{π}{4} (\int_{0}^{6} 36 d y - \int_{0}^{6} y^{2} d y)

\int_{0}^{6} 36 d y = 216

\int_{0}^{6} y^{2} d y = 72

= \frac{π}{4} (216 - 72)

Simplify

\frac{π}{4} (216 - 72) : 36 π

= 36 π

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What is the integral from 0 to 6 of pi/4 (36-y^2) ?
The integral from 0 to 6 of pi/4 (36-y^2) is 36pi