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

The integral from 0 to x of x^2y is (x^4)/2

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integral from 0 to x of x^2y

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

\frac{x ^{4}}{2}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{x ^{2}}{2}

= x^{2} \frac{x ^{2}}{2}

Simplify

= \frac{x ^{4}}{2}

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What is the integral from 0 to x of x^2y ?
The integral from 0 to x of x^2y is (x^4)/2