What is the integral from 1/4 to 1 of (32)/(x^3) ?

The integral from 1/4 to 1 of (32)/(x^3) is 240

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integral from 1/4 to 1 of (32)/(x^3)

\int_{\frac{1}{4}}^{1} \frac{32}{x ^{3}} d x

240

Solution steps

\int_{\frac{1}{4}}^{1} \frac{32}{x ^{3}} d x

Take the constant out:

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

= 32 \cdot \int_{\frac{1}{4}}^{1} \frac{1}{x ^{3}} d x

Apply the Power Rule

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

= 32 [- \frac{1}{2 x ^{2}}]_{\frac{1}{4}}^{1}

Compute the boundaries:

\frac{15}{2}

= 32 \cdot \frac{15}{2}

Simplify

= 240

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What is the integral from 1/4 to 1 of (32)/(x^3) ?
The integral from 1/4 to 1 of (32)/(x^3) is 240