F(x) = (1+x) between -1<x<0, and (1) between 0<x<1, does anyone know how to find a0 (For The Fourier Series)??

Answer 1

I1 = integration[(1+x)dx from -1 to 0]
= (x + x^2 / 2) from -1 to 0
= 0-(-1 + 1/2)
= 1/2 = 0.5
I2 = integration[1dx from 0 to 1]
= [x] from 0 to 1
= 1 - 0 = 1

Period T = 1 + 1 = 2

Fourier series
a0 = 1/T[I1 + I2}
= 1/2[0.5 + 1]
= 0.75

Answer 2

A0 is the just the average value. That should be easy.

Answer 3

x more than -1
x less than 0
so x = 0 to -1
it could be -0.5

x more than 0
x less than 1
so x could be from 0 to 1
it could be +0.5