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anonymous
 one year ago
Find the half range of cosine and sine expansion of:
f(x) = { 1, 0<x<1/2
{ 0, 1/2<x<1
anonymous
 one year ago
Find the half range of cosine and sine expansion of: f(x) = { 1, 0<x<1/2 { 0, 1/2<x<1

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The half range here is \(1\), so the cosine and sine expansions are given by \[2\int_0^1f(x)\cos nx\,dx\quad\text{and}\quad2\int_0^1f(x)\sin nx\,dx\](respectively). Compute these by splitting up the interval of integration; for example, \[2\int_0^1f(x)\cos nx\,dx=2\left(\int_0^{1/2}\cos nx\,dx+\int_{1/2}^1 0\,dx\right)=2\int_0^{1/2}\cos nx\,dx\] Can you take it from here?
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