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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

0

Solution steps

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

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

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

= \frac{8}{3} - \frac{8}{3}

Simplify

= 0

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