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

The integral from y^2 to y of 2y is y^2-y^4

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integral from y^2 to y of 2y

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

y^{2} - y^{4}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

Simplify

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

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\int_{0}^{1} 2 t \cdot 1 + 4 t^{2} d t

\int_{- 1}^{1} (x^{2} - 2 - x^{2}) d x

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