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October 22nd, 2017, 01:02 AM  #1 
Newbie Joined: Apr 2017 From: Bhadohi, U.P., India Posts: 26 Thanks: 1  Find the integrals using Leibnitz method of differentiation under integral sign
Try as many you can. Thank you.

October 22nd, 2017, 04:11 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
What do you get if you differentiate each of those integrands with respect to $\displaystyle \alpha$?

October 22nd, 2017, 04:47 AM  #3 
Newbie Joined: Apr 2017 From: Bhadohi, U.P., India Posts: 26 Thanks: 1  for question number 11
i get this after differentiating the given integral w.r.t. alpha and then integrating it w.r.t x. but it doesn't seems integrating it w.r.t. alpha will yield the required result (=π•alpha)
Last edited by Shariq Faraz; October 22nd, 2017 at 04:48 AM. Reason: spelling mistake 
October 22nd, 2017, 04:56 AM  #4 
Newbie Joined: Apr 2017 From: Bhadohi, U.P., India Posts: 26 Thanks: 1  for question number 14
i get this after differentiating the given integral w.r.t alpha and then integrating it w.r.t x .

October 22nd, 2017, 05:09 AM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
In both cases you have differentiated incorrectly. Leibniz's rule is that $\displaystyle \frac{d}{d\alpha}\left(\int_{u(\alpha)}^{v(\alpha) } f(x, \alpha)dx\right)= f(v(\alpha), \alpha)\frac{dv}{d\alpha}$$\displaystyle f(u(\alpha), \alpha)\frac{du}{d\alpha}+ \int_{u(\alpha)}^{v(\alpha)} \frac{\partial f(x, \alpha)}{\partial \alpha}dx$. 
October 22nd, 2017, 05:19 AM  #6 
Newbie Joined: Apr 2017 From: Bhadohi, U.P., India Posts: 26 Thanks: 1 
give me the solution please to anyone of the questions: que. 11 or 14

October 24th, 2017, 07:52 AM  #7 
Newbie Joined: Oct 2017 From: Texas Posts: 9 Thanks: 0  

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