What is the integral from 0 to x of 8xy ?

The integral from 0 to x of 8xy is 4x^3

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integral from 0 to x of 8xy

\int_{0}^{x} 8 x y d y

4 x^{3}

Solution steps

\int_{0}^{x} 8 x y d y

Take the constant out:

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

= 8 x \cdot \int_{0}^{x} y d y

Apply the Power Rule

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

= 8 x [\frac{y ^{2}}{2}]_{0}^{x}

Compute the boundaries:

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

= 8 x \frac{x ^{2}}{2}

Simplify

= 4 x^{3}

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What is the integral from 0 to x of 8xy ?
The integral from 0 to x of 8xy is 4x^3