Question

find the Fourier series of function f(x)=(π-x)​

Answer 1

Answer:

Step-by-step explanation:

f(x)=π−xx∈[0,2π[

a0=1π ∫2π0f(x) dx=1π ∫2π0(π−x) dx=0

an=1π ∫2π0cos(nx) dx=1π ∫2π0(π cos(nx)−x cos(nx)) dx=

1π ( [πn sin(nx)]2π0−[xn sin(nx)+1n2 cos(nx)]2π0)=0

bn=1π ( [ −πn cos(nx)]2π0−[−xn cos(nx)+1n2 sin(nx)]2π0)=2n

f(x)=2∑n=1+∞1n sin(nx)