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Integral Calculus

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29 Nov 2008 13:52:21 IST

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A tricky integral. Open to all.

None

Evaluate the integral

$I=\int_0^{\pi/2} \dfrac{\mathrm{d}x}{1+(\tan x)^{\sqrt{2}}}$

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Akshay Pamnani

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29 Nov 2008 14:14:14 IST

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is the answer pie/4??

abhishek sinha

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29 Nov 2008 15:18:18 IST

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The tricky thing is that, while evaluating it we can't use the usual law of indices ( because they are defined only for rational indices )

so write (tan x )^sqrt(2) as exp ( sqrt(2) ln tan x) ( e^x is defined for all real x)

Now apply the usual method ...

Ans will tuern out to be same with the " wrong " method , i.e. pi/4.

Anant Kumar

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29 Nov 2008 16:16:08 IST

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budku007

Would you supply the steps?

Anand

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29 Nov 2008 22:49:35 IST

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Can u show the steps please.

Anant Kumar

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30 Nov 2008 16:46:33 IST

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Sorry guys, . There's nothing tricky about it... you can use the normal rules. Actually, I did it by some obscure geometrical method and came to believe that that was the only way out.. :(

Anand

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30 Nov 2008 19:22:36 IST

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Sir,
Can you show your work.

Suchintan Mondal

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29 Aug 2009 17:49:52 IST

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let the given expression be I.

then I=integration (0 to pi/2) dx/(1+(cot x)^{sq root of 2}).( BY PROPERTY OF DEFINITE INTEGRAL)

then I+I=2I=integration (0 to pi/2) dx

implies I=pi/4

note: as there was problem in adding symbols I wrote it in words.Please forgive me if u hav any problem to read.

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