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

The integral from 1 to 3 of (x-1/(x^2)) is 10/3

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

\int_{1}^{3} (x - \frac{1}{x ^{2}}) d x

\frac{10}{3}

Decimal

3.33333 \dots

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{1}^{3} x d x = 4

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

= 4 - \frac{2}{3}

Simplify

4 - \frac{2}{3} : \frac{10}{3}

= \frac{10}{3}

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What is the integral from 1 to 3 of (x-1/(x^2)) ?
The integral from 1 to 3 of (x-1/(x^2)) is 10/3