# Thread: Parseval integration limits

1. ## Parseval integration limits

Hello,
Using Parseval's Theorem:
$\int_a^b f(x)^2 dx = 2\pi (\frac{a_0}{2})^2 + \sum_{n=1}^{\infty}[ a_{n}^2\pi + b_{n}^2\pi ]$
I know that a,b are usually $0,2\pi$ or $-\pi,\pi$, how does one determine their values?

2. Originally Posted by dudyu
Hello,
Using Parseval's Theorem:
$\int_a^b f(x)^2 dx = 2\pi (\frac{a_0}{2})^2 + \sum_{n=1}^{\infty}[ a_{n}^2\pi + b_{n}^2\pi ]$
I know that a,b are usually $0,2\pi$ or $-\pi,\pi$, how does one determine their values?
Look at how $a_n$ and $b_n$ are calculated (they are the same as the limits of integration there)

CB

3. Ah, my notations were misleading- the 'a' and 'b' in the integration have nothing to do with $a_n , b_b$ inside the sum.
Either that, or I didn't get what you meant:/

4. Originally Posted by dudyu
Ah, my notations were misleading- the 'a' and 'b' in the integration have nothing to do with $a_n , b_b$ inside the sum.
Either that, or I didn't get what you meant:/
Despite your careless notation I know that. My post asked how are the coefficients defined? Is there an integral there and what are the limits of integrations in those definitions?

CB