What is the integral from 0 to y^2 of x^2y ?

The integral from 0 to y^2 of x^2y is (y^7)/3

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integral from 0 to y^2 of x^2y

\int_{0}^{y^{2}} x^{2} y d x

\frac{y ^{7}}{3}

Solution steps

\int_{0}^{y^{2}} x^{2} y d x

Take the constant out:

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

= y \cdot \int_{0}^{y^{2}} x^{2} d x

Apply the Power Rule

= y [\frac{x ^{3}}{3}]_{0}^{y^{2}}

Compute the boundaries:

\frac{y ^{6}}{3}

= y \frac{y ^{6}}{3}

Simplify

= \frac{y ^{7}}{3}

What is the integral from 0 to y^2 of x^2y ?
The integral from 0 to y^2 of x^2y is (y^7)/3