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Integrate from 0 to infinity ∫[3/(x 2 +1)] dx [] denotes the greatest integer function..

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

Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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
10 Points
9 years ago
Thank u Jitender Sir.

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