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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

diverges

Solution steps

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

Find undefined (singularity) points:

x = 1

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

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

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{1}^{2} x e^{- 2 x^{2}} d x

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

\int_{0}^{5} 2 x^{2} d x

\int_{2}^{5} 2^{3 x} d x

\int_{0}^{2} x (x^{2} + 1)^{2} d x

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