(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi,

I must show that ([tex]\int cos(x)f(x)dx[/tex])^2 <= 2 [tex]\int cos(x)f(x)^2dx[/tex]

(the integrals are from -pi/2 to pi/2)

3. The attempt at a solution

I know that I should use cauchey-schwarz inequality to solve this where <f,g> = [tex]\int f(x)g(x)dx[/tex] In this case i just set g(x) = cos x

Therefore i get

([tex]\int cos(x)f(x)dx[/tex])^2 <= [tex]\int f(x)^2dx[/tex] [tex]\int cos^2(x)dx[/tex] I calculated then integral of cos^2(x) which is 1/2(x + sin(2x)/2) since cos^2(x) = (1 + cos(2x))/2

However this leaves me with pi/2 to get:

([tex]\int cos(x)f(x)dx[/tex])^2 <= pi/2 [tex]\int f(x)^2dx[/tex]

Howcome I am not getting the same answer as the one I should be proving, why does the question have a cos in the integral?

Thank you

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integral inequality

**Physics Forums | Science Articles, Homework Help, Discussion**