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

The integral from 1 to 3 of (3/(x^2)-1) is 0

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

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

0

Solution steps

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

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

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

= 2 - 2

Simplify

= 0

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What is the integral from 1 to 3 of (3/(x^2)-1) ?
The integral from 1 to 3 of (3/(x^2)-1) is 0