# Integral[abs(sen(x))*cos(n*x), x,- π , π ]

coredump62 shared this problem 5 years ago
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The command

Integral[abs(sen(x))*cos(n*x), x,- π , π ]

in CAS view is faulty, returns

((-2) * cos((n * π)) / (n^(2) - 1))

(((-2) * cos((n * π))) - 2) / (n^(2) - 1)

you can obtain it with

Integral[-sen(x)*cos(n*x), x, - π , 0 ] + Integral[sen(x)*cos(n*x), x, 0, π ]

Regards . . . And apologize my poor english.

Martín

[co]GeoGebra 5.0.253.0-3D (20 June 2016)

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That's due to the discontinuities in the function which are very difficult to deal with. If you use a specific value of "n" then you will get the correct answer 1

Yes, the second way ( Integral[-sen(x)*cos(n*x), x, - π , 0 ] + Integral[sen(x)*cos(n*x), x, 0, π ] ) works fine and avoid abs.

We're trying to calculate the general formulae for Fourier coeff. of a function, so we didn't want to work with a specific value of n. Thank very much for your answer. Regards,

Martín 