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

The integral from 0 to sqrt(2 of) pi/4 z^2 is pi/(3sqrt(2))

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

\int_{0}^{2} \frac{π}{4} z^{2} d z

\frac{π}{3 2}

Decimal

0.74048 \dots

Solution steps

\int_{0}^{2} \frac{π}{4} z^{2} d z

Take the constant out:

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

= \frac{π}{4} \cdot \int_{0}^{2} z^{2} d z

Apply the Power Rule

: [\frac{z ^{3}}{3}]_{0}^{2}

= \frac{π}{4} [\frac{z ^{3}}{3}]_{0}^{2}

Compute the boundaries:

\frac{2 2}{3}

= \frac{π}{4} \cdot \frac{2 2}{3}

Simplify

= \frac{π}{3 2}

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What is the integral from 0 to sqrt(2 of) pi/4 z^2 ?
The integral from 0 to sqrt(2 of) pi/4 z^2 is pi/(3sqrt(2))