Need help with deciphering calculus 2 problem
Question: Use the substitution cos(pi/2-x)=sinx to show that for any continuous function f,
[integral f(sinx)dx from 0 to pi/2]=[integral f(cosx)dx from 0 to pi/2].
My confusion is that f is inside the integral and I have no idea if it would change anything.
When I do the substitution normally I get [integral f(cosu)du from 0 to pi/2] but that doesn't help because it is in terms of u and not x.
Can someone help me understand this?
February 14, 2013
2 Comments • Newest first
[quote=Roxcibop]Just do the integral.
http://www.dropbox.com/s/mqaipadyot4knlv/20130213_231341.jpg[/quote]
Thanks. It was just my stupidity. I forgot that you have to change cos to sin when you flip the integrand with the negative. Kept getting -1=1.
[quote=Roxcibop]Just do the integral.
http://www.dropbox.com/s/mqaipadyot4knlv/20130213_231341.jpg[/quote]
Is that your handwriting?