What is the integral from z^2 to 8-z^2 of z^2 ?

The integral from z^2 to 8-z^2 of z^2 is (512-192z^2+24z^4-2z^6)/3

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integral from z^2 to 8-z^2 of z^2

\int_{z^{2}}^{8 - z^{2}} z^{2} d z

\frac{512 - 192 z ^{2} + 24 z ^{4} - 2 z ^{6}}{3}

Solution steps

\int_{z^{2}}^{8 - z^{2}} z^{2} d z

Apply the Power Rule

: [\frac{z ^{3}}{3}]_{z^{2}}^{8 - z^{2}}

= [\frac{z ^{3}}{3}]_{z^{2}}^{8 - z^{2}}

Compute the boundaries:

\frac{( 8 - z ^{2} ) ^{3}}{3} - \frac{z ^{6}}{3}

= \frac{( 8 - z ^{2} ) ^{3}}{3} - \frac{z ^{6}}{3}

Simplify

= \frac{512 - 192 z ^{2} + 24 z ^{4} - 2 z ^{6}}{3}

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What is the integral from z^2 to 8-z^2 of z^2 ?
The integral from z^2 to 8-z^2 of z^2 is (512-192z^2+24z^4-2z^6)/3