Can you think of a different way?

Any way you can calculate this integral
#int_0^(pi/4)(sqrt(1+cosx)) dx#
without using the trigonometric identity #1+cosx=2cos^2(x/2)# ?

1 Answer
Feb 2, 2018

Please see below.

Explanation:

#sqrt(1+cosx) = sqrt(1+cosx) * sqrt(1-cosx)/sqrt(1-cosx)#

# = sqrt(sin^2x)/sqrt(1-cosx)#

# = abs(sinx)/sqrt(1-cosx)#

So,

#int_0^(pi/4) sqrt(1+cosx) dx = int_0^(pi/4) (sinx)/sqrt(1-cosx) dx#

Now use #u = 1-cosx#