Integration Marathon
Posted: Mon Apr 05, 2021 12:37 am
Just like differentiation marathon, here's the integration marathon. Rules are same.
Let's start by a BdMO problem.
$\text{Problem 0 :}$
Evaluate
\[\int_0^{\frac{\pi}{2}}\frac{\cos^4x+\sin{x}\cos^3x+\sin^2{x}\cos^2x+\sin^3x\cos{x}}{\sin^4x+\cos^4x+2\sin{x}\cos^3x+2\sin^2x\cos^2x+2\sin^3x\cos{x}}dx\]
Source :
Let's start by a BdMO problem.
$\text{Problem 0 :}$
Evaluate
\[\int_0^{\frac{\pi}{2}}\frac{\cos^4x+\sin{x}\cos^3x+\sin^2{x}\cos^2x+\sin^3x\cos{x}}{\sin^4x+\cos^4x+2\sin{x}\cos^3x+2\sin^2x\cos^2x+2\sin^3x\cos{x}}dx\]
Source :