What is the integral from x^2 to 2x of 4xy ?

The integral from x^2 to 2x of 4xy is 4x(2x^2-(x^4)/2)

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integral from x^2 to 2x of 4xy

\int_{x^{2}}^{2 x} 4 x y d y

4 x (2 x^{2} - \frac{x ^{4}}{2})

Solution steps

\int_{x^{2}}^{2 x} 4 x y d y

Take the constant out:

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

= 4 x \cdot \int_{x^{2}}^{2 x} y d y

Apply the Power Rule

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

= 4 x [\frac{y ^{2}}{2}]_{x^{2}}^{2 x}

Compute the boundaries:

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

= 4 x (2 x^{2} - \frac{x ^{4}}{2})

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