help@askiitians.com

1800-150-456-789

Integral Calculus> Integrate from 0 to infinity ∫[3/(x 2 +1)...

question mark

Integrate from 0 to infinity
∫[3/(x²+1)] dx
[] denotes the greatest integer function..

Lovey , 10 Years ago

Grade 12

2 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int_{0}^{\infty }[\frac{3}{x^{2} + 1}]dx$
Here,
$0 < \frac{3}{x^{2} + 1}\leq 3$
$\frac{3}{x^{2} + 1} = 2$
$\Rightarrow x = \frac{1}{\sqrt{2}}$
$\frac{3}{x^{2} + 1} = 1$
$\Rightarrow x = \sqrt{2}$
$I = \int_{0}^{1/\sqrt{2}}2dx + \int_{1/\sqrt{2}}^{\sqrt{2}}1.dx + \int_{\sqrt{2}}^{\infty }0dx$
$I = \sqrt{2} + \sqrt{2} - \frac{1}{\sqrt{2}}$
$I = \frac{3}{\sqrt{2}}$

Lovey

Last Activity: 10 Years ago

Thank u Jitender Sir.

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

The area of a square field is 640000cm².what is its area in hectares

integral calculus

1 Answer Available

Last Activity: 2 Years ago

Please solve this integration. I am facing difficulty in it
How to solve this. Please solve anyone. Humble request

integral calculus

0 Answer Available

Last Activity: 3 Years ago

Using laplace transform, solve d²y/dt²+ dy/dt = t² +2t given that y=4 and y’=-2 and t=0

integral calculus

0 Answer Available

Last Activity: 3 Years ago

how to solve this?
this is interger type question .

integral calculus

0 Answer Available

Last Activity: 3 Years ago

View all Questions