MediumCalculusca-086

Fourier Sine Coefficient

Problem

For f(x) = x on the interval (0, pi), the Fourier sine coefficients are b_n = (2/pi) * integral from 0 to pi of x*sin(n*x) dx.

Integration by parts gives b_n = 2 * (-1)^(n+1) / n. Return b_n for a given positive integer n.

Hint

The integral of x sin(nx) over one period produces a factor cos(n*pi) = (-1)^n.

case 1

in: [1]

expected: 2

case 2

in: [2]

expected: -1

case 3

in: [3]

expected: 0.6666666666666666

case 4

in: [4]

expected: -0.5

case 5

in: [5]

expected: 0.4

Starter codePython

def fourier_sine_x(n):
    # Your code here
    pass

5 test cases · run your code against them in the editor