Question

find the fourier series representation of f(x)=x + 1 for -1less than or equal to x less than or equal to 1

Answer 1

Have you considered doing the work?

\(a_{0} = \int\limits_{-1}^{1}(x+1)\;dx = 2\)

With that transformation, it magically turns into an Odd Function about y = 1, so we can forget about all the rest of the \(a_{i}\).

\(b_{1} = \int\limits_{-1}^{1}(x+1)\cdot\sin(\pi\;x)\;dx\;=\;\dfrac{2}{\pi}\).

Likewise, \(b_{2} = \int\limits_{-1}^{1}(x+1)\cdot\sin(2\pi\;x)\;dx\;=\;-\dfrac{1}{\pi}\).

You're almost done!

Answer 2

so does it mean i should the subtitute the result into f(x)=1ao/2 + sum( an cos nx t bn sinnx )
please can you complete the solving for me please

Answer 3

Yes, that is the right formula, however:
1) Pay attention. All the \(a_{n} = 0\), excepting the first.
2) Feel free to do your own integrals. You'll see a pattern, soon enough.

Answer 4

i got f(x) = 1+1cosxsinx/pi -2cosxsinx/pi........ am i correct . if not please help with the solution

Answer 5

Not quite. cos(x) is incorrect in both. There is other stuff in the argument.