# integration problem

• May 20th 2010, 04:10 AM
prasum
integration problem
how to integrate y=(1+sin2x)/(cosx+sinx)between x=0 and x=45(in degrees)
• May 20th 2010, 04:53 AM
mr fantastic
Quote:

Originally Posted by prasum
how to integrate y=(1+sin2x)/(cosx+sinx)between x=0 and x=45(in degrees)

Prove the following identity: $\frac{1 + \sin (2x)}{\cos (x) + \sin (x)} = \cos (x) + \sin (x)$.

Now the integration is trivial.
• May 20th 2010, 05:24 AM
prasum
thanks for the suggestion. please tell me how to prove the identity(Wink)
• May 20th 2010, 07:10 AM
harish21
Quote:

Originally Posted by prasum
thanks for the suggestion. please tell me how to prove the identity(Wink)

$\frac{1+sin(2x)}{cosx+sinx} \times \frac{cosx+sinx}{cosx+sinx}$

Now simplify.

I hope you know that sin2x = 2sinx.cosx