IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

anandghegde

Is the question $\int \frac{\sqrt{1-\sin x}}{1+\cos x}.e^{\frac{-x}{2}} dx$ ??

if yes, then its very easy

$I = \int \frac{\sqrt{\sin^2 \frac{x}{2}+\cos^2 \frac{x}{2}-2\sin \frac{x}{2}\cos \frac{x}{2}}}{2 \cos^2 \frac{x}{2}}.e^{\frac{-x}{2}} dx$

$I = \int \frac{\sin \frac{x}{2} - \cos \frac{x}{2}}{2 \cos^2 \frac{x}{2}}.e^{\frac{-x}{2}} dx$

Strictly speaking, it should be $\mid \sin \frac{x}{2} - \cos \frac{x}{2} \mid$

$I =\frac{1}{2} \int (\tan \frac{x}{2}.\sec \frac{x}{2}- \sec \frac{x}{2}) . e^{\frac{-x}{2} dx$

which is equal to $e^{\frac{-x}{2}}. \sec \frac{x}{2} + c$

Ask & Discuss Questions with Community & Experts