What is the integral from 1/4 to 1/2 of 2x^3 ?

The integral from 1/4 to 1/2 of 2x^3 is 15/512

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integral from 1/4 to 1/2 of 2x^3

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

\frac{15}{512}

Decimal Notation

0.029296875

Solution steps

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

Take the constant out:

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

= 2 \cdot \int_{\frac{1}{4}}^{\frac{1}{2}} x^{3} d x

Apply the Power Rule

: [\frac{x ^{4}}{4}]_{\frac{1}{4}}^{\frac{1}{2}}

= 2 [\frac{x ^{4}}{4}]_{\frac{1}{4}}^{\frac{1}{2}}

Compute the boundaries:

\frac{15}{1024}

= 2 \cdot \frac{15}{1024}

Simplify

= \frac{15}{512}

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What is the integral from 1/4 to 1/2 of 2x^3 ?
The integral from 1/4 to 1/2 of 2x^3 is 15/512