What is the integral from 4 to 8 of 3/(x^3) ?

The integral from 4 to 8 of 3/(x^3) is 9/128

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integral from 4 to 8 of 3/(x^3)

\int_{4}^{8} \frac{3}{x ^{3}} d x

\frac{9}{128}

Solution steps

\int_{4}^{8} \frac{3}{x ^{3}} d x

Take the constant out:

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

= 3 \cdot \int_{4}^{8} \frac{1}{x ^{3}} d x

Apply the Power Rule

: [- \frac{1}{2 x ^{2}}]_{4}^{8}

= 3 [- \frac{1}{2 x ^{2}}]_{4}^{8}

Compute the boundaries:

\frac{3}{128}

= 3 \cdot \frac{3}{128}

Simplify

= \frac{9}{128}

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What is the integral from 4 to 8 of 3/(x^3) ?
The integral from 4 to 8 of 3/(x^3) is 9/128