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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. |
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Answer» `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 |
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