What is the integral from y^2 to 1 of 4y ?

The integral from y^2 to 1 of 4y is 2(-y^4+1)

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integral from y^2 to 1 of 4y

\int_{y^{2}}^{1} 4 y d y

2 (- y^{4} + 1)

Solution steps

\int_{y^{2}}^{1} 4 y d y

Take the constant out:

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

= 4 \cdot \int_{y^{2}}^{1} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{y^{2}}^{1}

= 4 [\frac{y ^{2}}{2}]_{y^{2}}^{1}

Compute the boundaries:

\frac{1}{2} - \frac{y ^{4}}{2}

= 4 (\frac{1}{2} - \frac{y ^{4}}{2})

Simplify

= 2 (- y^{4} + 1)

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What is the integral from y^2 to 1 of 4y ?
The integral from y^2 to 1 of 4y is 2(-y^4+1)