What is the integral from x^3 to 8 of 2xy ?

The integral from x^3 to 8 of 2xy is 64x-x^7

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integral from x^3 to 8 of 2xy

\int_{x^{3}}^{8} 2 x y d y

64 x - x^{7}

Solution steps

\int_{x^{3}}^{8} 2 x y d y

Take the constant out:

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

= 2 x \cdot \int_{x^{3}}^{8} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{x^{3}}^{8}

= 2 x [\frac{y ^{2}}{2}]_{x^{3}}^{8}

Compute the boundaries:

32 - \frac{x ^{6}}{2}

= 2 x (32 - \frac{x ^{6}}{2})

Simplify

= 64 x - x^{7}

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What is the integral from x^3 to 8 of 2xy ?
The integral from x^3 to 8 of 2xy is 64x-x^7