What is the integral from-2 to 5 of x/(x^2-4) ?

The integral from-2 to 5 of x/(x^2-4) is diverges

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-2 to 5 of x/(x^2-4)

\int_{- 2}^{5} \frac{x}{x ^{2} - 4} d x

diverges

Solution steps

\int_{- 2}^{5} \frac{x}{x ^{2} - 4} d x

Find undefined (singularity) points:

x = 2

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_{- 2}^{2} \frac{x}{x ^{2} - 4} d x + \int_{2}^{5} \frac{x}{x ^{2} - 4} d x

\int_{- 2}^{2} \frac{x}{x ^{2} - 4} d x = 0

\int_{2}^{5} \frac{x}{x ^{2} - 4} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{2}^{3} (x^{2}) d x

\int_{0}^{π} sin (z) d z

\int_{1}^{e} \frac{( x ^{2} + 1 ) ln ( x )}{x} d x

\int_{0}^{2} 0.5 d x

\int_{0}^{1} x^{2} 6 x + 9 d x

What is the integral from-2 to 5 of x/(x^2-4) ?
The integral from-2 to 5 of x/(x^2-4) is diverges