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

The integral from z^2 to 8-z^2 of z is 8(-z^2+4)

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

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

8 (- z^{2} + 4)

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{( 8 - z ^{2} ) ^{2}}{2} - \frac{z ^{4}}{2}

= \frac{( 8 - z ^{2} ) ^{2}}{2} - \frac{z ^{4}}{2}

Simplify

= 8 (- z^{2} + 4)

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What is the integral from z^2 to 8-z^2 of z ?
The integral from z^2 to 8-z^2 of z is 8(-z^2+4)