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

The integral from 1 to 3 of x^2-1/(x^2) is 8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

8

Solution steps

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

\int_{1}^{3} x^{2} d x = \frac{26}{3}

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

= \frac{26}{3} - \frac{2}{3}

Simplify

\frac{26}{3} - \frac{2}{3} : 8

= 8

\int_{- 1}^{3} (4 x^{2} - 3 x - 2)^{2} d x

\int_{- 2}^{0} \frac{1}{x ^{2}} d x

\int_{0}^{2 π} (- sin^{2} (t)) d t

\int_{1}^{e} \frac{( x ^{3} + 1 )}{x} d x

\int_{0}^{\frac{π}{2}} (sin (t)) d t

What is the integral from 1 to 3 of x^2-1/(x^2) ?
The integral from 1 to 3 of x^2-1/(x^2) is 8