integration problem

Feb 2010
460
37
how to integrate y=(1+sin2x)/(cosx+sinx)between x=0 and x=45(in degrees)
 

mr fantastic

MHF Hall of Fame
Dec 2007
16,948
6,768
Zeitgeist
how to integrate y=(1+sin2x)/(cosx+sinx)between x=0 and x=45(in degrees)
Prove the following identity: \(\displaystyle \frac{1 + \sin (2x)}{\cos (x) + \sin (x)} = \cos (x) + \sin (x)\).

Now the integration is trivial.
 
Feb 2010
460
37
thanks for the suggestion. please tell me how to prove the identity(Wink)
 
Feb 2010
1,036
386
Dirty South
thanks for the suggestion. please tell me how to prove the identity(Wink)
\(\displaystyle \frac{1+sin(2x)}{cosx+sinx} \times \frac{cosx+sinx}{cosx+sinx}\)

Now simplify.

I hope you know that sin2x = 2sinx.cosx