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I know I am missing something simple from this integration.

integrate from l to -l

[tex]\int[/tex]cos ((k*pi*x)/l) * cos ((k*pi*x)/l)dx

I use the identity cos u cos v = 1/2 [cos(u-v) + cos(u+v)]

which gives me the following to integrate from l to -l

1/2[cos (2k*pi*x)/l]dx

I bring 1/2 out of integration

so when i integrate [cos (2k*pi*x)/l]dx

i get [sin (2k*pi*x)/l] / [(2k*pi)/l]

now i move the numerator out so the outside becomes l/4*k*pi

and the inside is [sin 2*k*pi + sin 2*k*pi]

Now my problem is this sin 2 k pi is zero

hence if i multiply it by the outside it will become zero but the answer is l

I know I am missing a simple step but dont know where.

Thanks guys

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# Missing something simple

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