Question

What is the value of a0 if the function is f(x) = x^3 in the interval 0 to 5?

(a) 25/4

(b) 125/4

(c) 625/4

(d) 5/4

This question was addressed to me during an online interview.

Query is from Fourier Half Range Series in portion Fourier Series of Engineering Mathematics

Answer 1

Correct answer is (c) 625/4

Explanation: \(\int_0^5 x^3 dx= \int_{-l}^l(f(x))^2 dx=l[\frac{a_0^2}{2}+∑_{n=1}^∞(a_n^2+b_n^2)] \) (from 0 to 5)

= \(\frac{5^4}{4}= \frac{625}{4}.\)