Integral calculus - +2 maths book

Question

When evaluating definite integrals for odd functions the answer will come as 0 as equal areas symmetric to x-axis will cancel out and give 0.But then should we take the modulus values and add?If area is asked then definitely we should do that.Please have a look at the question below and comment.I am getting answer as 0 but if I take mod values by splitting intervals then I get the answer as 2 log 2 which is given.

Comments

This is the integral

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What is the correct answer?

Answer 1

Yes, while evaluating definite integrals for odd functions is always zero. But if area is asked then we should take modulus and add.

In definite integral if you split the interval then + or - sign is to be placed before the integral depending upon the behavior of that function in that interval. 

Here is my solution

Comments

thanks buddy....actually I had transformed the function so I was not getting the condition for odd functions properly....yes given answer is 2 ln 2.