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

The integral from x to 2x of xy^3 is x(4x^4-(x^4)/4)

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integral from x to 2x of xy^3

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

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What is the integral from x to 2x of xy^3 ?
The integral from x to 2x of xy^3 is x(4x^4-(x^4)/4)