What is the integral from 0 to 2x of xy^3 ?

The integral from 0 to 2x of xy^3 is 4x^5

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integral from 0 to 2x of xy^3

\int_{0}^{2 x} x y^{3} d y

4 x^{5}

Solution steps

\int_{0}^{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_{0}^{2 x} y^{3} d y

Apply the Power Rule

: [\frac{y ^{4}}{4}]_{0}^{2 x}

= x [\frac{y ^{4}}{4}]_{0}^{2 x}

Compute the boundaries:

4 x^{4}

= x \cdot 4 x^{4}

Simplify

= 4 x^{5}

\int_{0}^{y} (x + y)^{2} d x

\int_{0}^{4} (x - 1)^{2} d x

\int_{2}^{4} \frac{1}{x ( ln ( x ) ) ^{3}} d x

\int_{- 4}^{3} \frac{1}{x ^{3}} d x

\int_{0}^{1} (x^{2} + 6) e^{5 x} d x

What is the integral from 0 to 2x of xy^3 ?
The integral from 0 to 2x of xy^3 is 4x^5