1.

Evaluate the integral (a)int_(-pi)^(pi) f(x) cos nx dx (b) int_(-pi)^(pi) f(x) sin nx dxf : (1) f(x) is an evenfunction ,(2) f(x) is an odd function.

Answer»


ANSWER :(1)if f (x)is an even function, then
`int_(-pi)^(pi) f(x) cos NX DX = 2 int_(0)^(pi) f(x) cos nx dx, and int_(-pi)^(pi) f(x) sin x dx = 0 `
(2)If f(x) is an odd function, then `int_(-pi)^(pi) f(x) cos nx dx = 0`, and`int_(-pi)^(pi)f(x) sin nx dx = 2 int_(0)^(pi) f(x)`sin n dx


Discussion

No Comment Found

Related InterviewSolutions