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

$= \frac{1}{2} (\frac{1}{3} π^2 )$

$= \frac{π^2}{6}$.