How do I find this integral?

  • Thread starter Math9999
  • Start date
  • #1
Math9999

Homework Statement


Find the integral of 1/(1+cosx) dx from -pi/2 to pi/2.

Homework Equations


None.

The Attempt at a Solution


Here's my work:
1/(1+cosx)=(1-cosx)/((1+cosx)(1-cosx))=(1-cosx)/(1-cos^2 x)=(1-cosx)/sin^2 x
This is what I've got so far. But this doesn't seem to simplify the integrand.
 

Answers and Replies

  • #2
PeroK
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Homework Statement


Find the integral of 1/(1+cosx) dx from -pi/2 to pi/2.

Homework Equations


None.

The Attempt at a Solution


Here's my work:
1/(1+cosx)=(1-cosx)/((1+cosx)(1-cosx))=(1-cosx)/(1-cos^2 x)=(1-cosx)/sin^2 x
This is what I've got so far. But this doesn't seem to simplify the integrand.
That looks good so far. What about splitting up the integral into two now?
 
  • #3
Math9999
Never mind. I got it. You gave me the big hint already, splitting it up.
 
  • #4
Math9999
Thank you so much! Merry Christmas!
 
  • #5
PeroK
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Homework Helper
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Gold Member
2020 Award
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Never mind. I got it. You gave me the big hint already, splitting it up.
There was a quicker way. Hint: ##x = 2(x/2)##.
 
  • #6
Math9999
Wow.
 

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