Please Some one provide me the Solution Of This Problem .

And

Please Some one provide me the Solution Of This Problem (2) .

And

Please Some one provide me the Solution Of This Problem (3)

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## Comments

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TopNewestHey guys please also solve the 3rd Problem.

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I have also added a new question Please check it Also If anyone can help me solving it.

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Have you got the second question??

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Can you post the solution of It.

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It is very easy. Just a matter of 5-6 steps. Use Ramanujan's Master Theorem. I'll provide a solution after 3 April.

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Please send Us solution Now. I need it. Please!

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My parents aren't allowing me to use PC. Shall I send you a pic through whatsapp?

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I had missed a term that's why I got it as infinity.

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Comment deleted Mar 28, 2016

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This question was in my Definite Integration Module . Yes it converges.

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I feel its somewhat related to Riemann Sums.But fortunately we have a cool guy in our community: @Rishabh Cool who will post an awesome solution to that problem :)

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Unfortunately I had tried that problem many times..... But I'm not able to find from where to start ..... Probably that integration sign is doing most of the harm... There might be a way to get rid of that integration sign.... Probably @Rishabh Deep Singh can help by telling what he has done to crack the problem.... DO you have a hint Nihar??

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Time to tag seniors: @Pi Han Goh @Ishan Singh @Aditya Kumar

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First question.Step 1) Notice that the integrand is an even function, so \( \displaystyle \int_{-\infty}^{\infty} \cdots = 2 \int_{0}^{\infty} \cdots \).

Step 2) Break the integral into two parts: \(\displaystyle 2 \int_{0}^{\infty} \cdots = 2 \int_{0}^{1} \cdots + 2 \int_{1}^{\infty} \cdots\).

Step 3) For the latter integral, try a substitution of \(y = 1/x\).

Step 4) Combine the 2 integrals into 1. Have you tried GP?

Step 5) Profit.

Second question.Do you know how to differentiate a Beta function? Differentiate through an integral

Step 1) \(\displaystyle B(a,b) = \dfrac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)} = \int_0^{\pi /2} (\sin x)^a (\cos x)^b \, dx \).

Step 2) Differentiiate both sides with respect to \(b\).

Step 3) What is the derivative of a Beta function?

Step 4) Profit.

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Correct me if I am wrong.

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