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Grade 12Integral Calculus

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

Lovey

11 Years agoGrade 12

2 Answers

Jitender Singh

Approved Tutor Answer11 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

11 Years ago

Thank u Jitender Sir.

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