Question

Find half range sine series of the function f(x) = x(π-x) in o

Answer 1

Answer:

Given f(x)=πx−x2(0,π)

Half range sine series is given by

bn=2l∫0πf(x)sinnxdx

bn=2π∫0πf(x)sinnxdx

bn=2π∫0π(πx−x2)sinnxdx

bn=2π[(πx−x2)(−cosnxn)−(π−2x)(−sinxn)+(−2)(cosnxn3)]π0

∴bn=2π[(0−0+(−2cosnπn3)−0+0+2n3)]

bn=2π(−2cosnπn3)+2n3

bn=2π[4n3]=8πn3 if n is odd

= 0 if n is ev

Answer 2

Answer:

8/π [1 + 1/27 + 1/125 + 1/343 +......]