1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Finding The Definite Integral

  1. Mar 27, 2017 #1
    1. The problem statement, all variables and given/known data
    Today i had a test on definite integrals which i failed. The test paper was given to us so we can practise at home and prepare better for the next one. This is the first problem which i need your help in solving::

    2. Relevant equations
    3. The attempt at a solution

    As no points were given for a solution of the below integrals without the proof of the integral property above i need to do that first. I had no idea how to start the proof. I figured i need to use some sort of substitution but i fail to see which and why. Could you give me a hint on how to do this? I know i haven't provided any work done by myself but i can't since i can't start. I didn't have a clue calculus was going to be this hard :/.
  2. jcsd
  3. Mar 27, 2017 #2
    The key here is that ##sin(x)## is symmetric around ##pi/2##. Hence the substitution ##t=pi/2+x## may be of use. You then see that a term in your new expression should disappear.
  4. Mar 27, 2017 #3


    User Avatar
    Science Advisor
    Homework Helper

    I think you probably meant something more like ##x=\pi-t##.
  5. Mar 27, 2017 #4
    The substitution ##x = \pi - t ## does indeed do the trick for proving the proposition before solving the given integral.
  6. Mar 27, 2017 #5
    Yeah i did it with the substitution you proposed but how did you arrive at it?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted