BDMO National Higher Secondary 2018/7

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nahin munkar
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BDMO National Higher Secondary 2018/7

Unread post by nahin munkar » Tue Jan 08, 2019 5:55 pm

Evaluate

$\int^{\pi/2}_0 \frac{\cos^4x + \sin x \cos^3 x + \sin^2x\cos^2x + \sin^3x\cos x}{\sin^4x + \cos^4x + 2\ sinx\cos^3x + 2\sin^2x\cos^2x + 2\sin^3x\cos x} dx$
# Mathematicians stand on each other's shoulders. ~ Carl Friedrich Gauss

samiul_samin
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Joined: Sat Dec 09, 2017 1:32 pm

Re: BDMO National Higher Secondary 2018/7

Unread post by samiul_samin » Sun Feb 10, 2019 10:54 am

Answer


$\dfrac{\pi}{4}$

Short solution
After a bit manipulation we can get the given expression as below
Screenshot_2019-02-10-11-02-23-1.png


and then we can easily get the answer.
Screenshot_2019-02-10-10-48-07-1.png
As writing the full solution is very time consuming ,I am not posting the full solution.Screenshot is taken from www.wolframalpha.com .

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

Re: BDMO National Higher Secondary 2018/7

Unread post by samiul_samin » Mon Feb 25, 2019 12:25 am

An interesting solution is available here.

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