What is the integral from 0 to 4 of pi(sqrt(y))^2 ?

The integral from 0 to 4 of pi(sqrt(y))^2 is pi8

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integral from 0 to 4 of pi(sqrt(y))^2

\int_{0}^{4} π (y)^{2} d y

π 8

Decimal

25.13274 \dots

Solution steps

\int_{0}^{4} π (y)^{2} d y

Take the constant out:

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

= π \cdot \int_{0}^{4} (y)^{2} d y

Simplify

(y)^{2} : y

= π \cdot \int_{0}^{4} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{0}^{4}

= π [\frac{y ^{2}}{2}]_{0}^{4}

Compute the boundaries:

8

= π 8

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What is the integral from 0 to 4 of pi(sqrt(y))^2 ?
The integral from 0 to 4 of pi(sqrt(y))^2 is pi8