Integrals

Question

I'm getting "not defined" .. 

Comments

https://gateoverflow.in/802/gate2009-25

here sir , after solving this reduces to my problem according to which answer should be not defined but answer is finite .... where did i go wrong ? thanks in advance :)

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I have posted my solution. You just reached to second last step and by multiply and divide you again went far from the last step. Please check out my solution you'll notice the steps.

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One doubt sir why integration formula already defined for sec2x and tan2x ot applicable here ?

Answer 1

Here is my solution answer is ln 2/2

Comments

yes sir that's right but at second step in your solution it gets converted to my problem isn't it and then it gives undefined result :(

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Initially I thought the same infact initally i directly took integration of sec x and tan x but that's not the way, bcz here in 2nd step we cannot put the limits directly. we need to evaluate it first and then only we can put the limits.

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thank you :)