Parseval 's Relation (or) Theorem (or) Identity

PARSEVAL'S RELATION (or) THEOREM (or) IDENTITY

Definition: Root Mean Square Value [RMS Value] (or) Effective value

Note: Parseval's theorem gives the values of root mean square of f (x) in terms of its Fourier coefficients.

Problems based on Parseval's theorem

Example 2.5.1: Obtain the Fourier series expansion of f (x) = x²(-1, 1). Find the sum of 

Example 2.5.2: Find the sine series for f (x) = x in 0 < x <л. 

Example 2.5.3: Find the Fourier series x2 in (– л, л). Use Parsevals

Example 2.5.4 : Find the cosine series for f (x) = x in (0, л) and then using Parseval's theorem.

Example 2.5.5: Find the half range cosine series of f (x) = (x − x²) in the interval (0,л). Hence find the sum of the

Example 2.5.6: Find the half-range cosine series for the function f(x) = x(x − x) in 0 < x < л. Deduce that