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

The integral from 0 to 2 of pi(y^2)^2 is (32pi)/5

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

\int_{0}^{2} π (y^{2})^{2} d y

\frac{32 π}{5}

Decimal

20.10619 \dots

Solution steps

\int_{0}^{2} π (y^{2})^{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}^{2} (y^{2})^{2} d y

Simplify

(y^{2})^{2} : y^{4}

= π \cdot \int_{0}^{2} y^{4} d y

Apply the Power Rule

: [\frac{y ^{5}}{5}]_{0}^{2}

= π [\frac{y ^{5}}{5}]_{0}^{2}

Compute the boundaries:

\frac{32}{5}

= π \frac{32}{5}

Simplify

= \frac{32 π}{5}

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What is the integral from 0 to 2 of pi(y^2)^2 ?
The integral from 0 to 2 of pi(y^2)^2 is (32pi)/5