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

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

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integral from-y to y^2 of 8y

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

4 (y^{4} - y^{2})

Solution steps

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

Take the constant out:

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

= 8 \cdot \int_{- y}^{y^{2}} y d y

Apply the Power Rule

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

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

Compute the boundaries:

\frac{y ^{4}}{2} - \frac{y ^{2}}{2}

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

Simplify

= 4 (y^{4} - y^{2})

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