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

The integral from z to 2-z^2 of z is (z^4-5z^2+4)/2

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integral from z to 2-z^2 of z

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

\frac{z ^{4} - 5 z ^{2} + 4}{2}

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

Simplify

= \frac{z ^{4} - 5 z ^{2} + 4}{2}

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What is the integral from z to 2-z^2 of z ?
The integral from z to 2-z^2 of z is (z^4-5z^2+4)/2