What is the integral from z^2 to 36-3z^2 of z ?

The integral from z^2 to 36-3z^2 of z is 4(z^4-27z^2+162)

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integral from z^2 to 36-3z^2 of z

\int_{z^{2}}^{36 - 3 z^{2}} z d z

4 (z^{4} - 27 z^{2} + 162)

Solution steps

\int_{z^{2}}^{36 - 3 z^{2}} z d z

Apply the Power Rule

= [\frac{z ^{2}}{2}]_{z^{2}}^{36 - 3 z^{2}}

Compute the boundaries:

\frac{( 36 - 3 z ^{2} ) ^{2}}{2} - \frac{z ^{4}}{2}

= \frac{( 36 - 3 z ^{2} ) ^{2}}{2} - \frac{z ^{4}}{2}

Simplify

= 4 (z^{4} - 27 z^{2} + 162)

What is the integral from z^2 to 36-3z^2 of z ?
The integral from z^2 to 36-3z^2 of z is 4(z^4-27z^2+162)