What is the integral from 1/2 to 1 of 8/(x^3) ?

The integral from 1/2 to 1 of 8/(x^3) is 12

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integral from 1/2 to 1 of 8/(x^3)

\int_{\frac{1}{2}}^{1} \frac{8}{x ^{3}} d x

12

Solution steps

\int_{\frac{1}{2}}^{1} \frac{8}{x ^{3}} d x

Take the constant out:

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

= 8 \cdot \int_{\frac{1}{2}}^{1} \frac{1}{x ^{3}} d x

Apply the Power Rule

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

= 8 [- \frac{1}{2 x ^{2}}]_{\frac{1}{2}}^{1}

Compute the boundaries:

\frac{3}{2}

= 8 \cdot \frac{3}{2}

Simplify

= 12

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What is the integral from 1/2 to 1 of 8/(x^3) ?
The integral from 1/2 to 1 of 8/(x^3) is 12