Question

Find bn when we have to find the half range sine series of the function x^2 in the interval 0 to 3.

(a) -18 \( \frac{cos(nπ)}{nπ} \)

(b) 18 \( \frac{cos(nπ)}{nπ} \)

(c) -18 \( \frac{cos(n \pi⁄2)}{nπ} \)

(d) 18 \( \frac{cos(n \pi⁄2)}{nπ} \)

I have been asked this question during an internship interview.

This intriguing question originated from Fourier Half Range Series in chapter Fourier Series of Engineering Mathematics

Answer 1

The correct answer is (a) -18 \( \frac{cos(nπ)}{nπ} \)

To explain I would say: bn = \(\frac{2}{3} \int_0^3 x^{2} sin\left(n\pi\frac{x}{3}\right)dx \)

= \(\frac{2}{3} \left(-27\frac{cos(nπ)}{nπ}\right) \)

= \(  -18\frac{cos(nπ)}{nπ}.\)