## BDMO National Higher Secondary 2018/7

nahin munkar
Posts: 81
Joined: Mon Aug 17, 2015 6:51 pm
Location: banasree,dhaka

### BDMO National Higher Secondary 2018/7

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

### Re: BDMO National Higher Secondary 2018/7

$\dfrac{\pi}{4}$

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

An interesting solution is available here.