What is the integral from 2 to 10 of k/(x^3) ?

The integral from 2 to 10 of k/(x^3) is (3k)/(25)

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integral from 2 to 10 of k/(x^3)

\int_{2}^{10} \frac{k}{x ^{3}} d x

\frac{3 k}{25}

Solution steps

\int_{2}^{10} \frac{k}{x ^{3}} d x

Take the constant out:

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

= k \cdot \int_{2}^{10} \frac{1}{x ^{3}} d x

Apply the Power Rule

: [- \frac{1}{2 x ^{2}}]_{2}^{10}

= k [- \frac{1}{2 x ^{2}}]_{2}^{10}

Compute the boundaries:

\frac{3}{25}

= k \frac{3}{25}

Simplify

= \frac{3 k}{25}

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What is the integral from 2 to 10 of k/(x^3) ?
The integral from 2 to 10 of k/(x^3) is (3k)/(25)