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

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

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

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

0

Solution steps

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

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

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

= 8 - 8

Simplify

= 0

\int_{- 2}^{2} 3 x^{8} - 2 d x

\int_{- 3}^{0} (x + 3)^{2} d x

\int_{0}^{2} x f (x^{2}) d x

\int_{- 2}^{2} x - \frac{4}{x} d x

\int_{- t}^{t} t d t

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