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October 22nd, 2017, 01:02 AM   #1
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Find the integrals using Leibnitz method of differentiation under integral sign

Try as many you can. Thank you.
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October 22nd, 2017, 04:11 AM   #2
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What do you get if you differentiate each of those integrands with respect to $\displaystyle \alpha$?
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October 22nd, 2017, 04:47 AM   #3
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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)
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Last edited by Shariq Faraz; October 22nd, 2017 at 04:48 AM. Reason: spelling mistake
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October 22nd, 2017, 04:56 AM   #4
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for question number 14

i get this after differentiating the given integral w.r.t alpha and then integrating it w.r.t x .
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October 22nd, 2017, 05:09 AM   #5
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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$.
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October 22nd, 2017, 05:19 AM   #6
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give me the solution please to anyone of the questions: que. 11 or 14
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October 24th, 2017, 07:52 AM   #7
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Hey

I think you should check out Integration Formulas
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