Question

Find  a0 of the function \(f(x) = \frac{1}{4} (π-x)^2.\)

(a) \(\frac{π^2}{6} \)

(b) \(\frac{π^2}{12} \)

(c) \(5\frac{π^2}{6} \)

(d) \(5\frac{π^2}{12} \)

I have been asked this question in class test.

I'd like to ask this question from Fourier Series Expansions in chapter Fourier Series of Engineering Mathematics

Answer 1

The correct answer is (a) \(\frac{π^2}{6} \)

To explain: \(f(x) = \frac{1}{4} (π-x)^2 \)

\(a_0 = \frac{1}{π} \int_0^{2π} \frac{1}{4} (π-x)^2 \)

= from 0 to 2 π

\( = \frac{1}{2} (\frac{1}{3} π^2 ) \)

\( = \frac{π^2}{6} \).