- #1
TyroneTheDino
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Homework Statement
Use the substitution ##u=\frac{\pi} {2}-x## evaluate the integral ##\int_0^\frac {\pi}{2} \frac {\sin x}{\cos x + \sin x}dx##.
Homework Equations
[/B]
##\cos (\frac {\pi}{2}-x)=\sin x##
The Attempt at a Solution
[/B]I start by plugging "u" into the equation making the function become
##\int_0^\frac {\pi}{2} \frac {\sin( \frac{\pi} {2}-x)}{\cos(\frac{\pi} {2}-x) + \sin (\frac{\pi} {2}-x)}##.
I substitute the sin x for the ##\cos (\frac {\pi}{2}-x)## because I know they are equal.
Then i have
##\int_0^\frac {\pi}{2} \frac {\sin (\frac{\pi} {2}-x)}{\sin (x) + \sin (\frac{\pi} {2}-x)}##
What comes next is a mystery to me.
I feel maybe I did not use the substitution in a correct way which is why am puzzled about were to go next.
I know that the answer is pi/4, but I'm not sure how to actually get there with substitutions.
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