Question

(R/2
1. The value of the definite integration
sin 2x - olds, where o € (0,7) is
A. 1 B. Cosa
C.
1 + cosa
2
D. (1 + sin (r)​

Answer 1

I=∫0π1+cosαsinxxdx

⇒I=∫0π1+cosαsin(π−x)π−xdx

∴2I=π∫0π1+cosαsinx1dx

⇒2I=π∫0π(1+tan22x)+2cosαtan21sec22xdx

Substitute tan2x=t⇒sec22xdx=2dt

∴2I=∫0∞1+t2+2tcosα2dt=2π∫0∞