What is the integral from 0 to x of x^3y^2 ?

The integral from 0 to x of x^3y^2 is (x^6)/3

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integral from 0 to x of x^3y^2

\int_{0}^{x} x^{3} y^{2} d y

\frac{x ^{6}}{3}

Solution steps

\int_{0}^{x} x^{3} y^{2} d y

Take the constant out:

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

= x^{3} \cdot \int_{0}^{x} y^{2} d y

Apply the Power Rule

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

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

Compute the boundaries:

\frac{x ^{3}}{3}

= x^{3} \frac{x ^{3}}{3}

Simplify

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

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What is the integral from 0 to x of x^3y^2 ?
The integral from 0 to x of x^3y^2 is (x^6)/3