What is the integral from 0 to y of 10xy^2 ?

The integral from 0 to y of 10xy^2 is 5y^4

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integral from 0 to y of 10xy^2

\int_{0}^{y} 10 x y^{2} d x

5 y^{4}

Solution steps

\int_{0}^{y} 10 x y^{2} d x

Take the constant out:

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

= 10 y^{2} \cdot \int_{0}^{y} x d x

Apply the Power Rule

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

= 10 y^{2} [\frac{x ^{2}}{2}]_{0}^{y}

Compute the boundaries:

\frac{y ^{2}}{2}

= 10 y^{2} \frac{y ^{2}}{2}

Simplify

= 5 y^{4}

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What is the integral from 0 to y of 10xy^2 ?
The integral from 0 to y of 10xy^2 is 5y^4