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Math Help - Please help with calculus fourier problem

  1. #1
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    Please help with calculus fourier problem

    I have included a pdf attachment I made with mathematica to help try and explain my problem.

    please help if you can..


    Merlyn.
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  2. #2
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    Quote Originally Posted by mercou View Post
    I have included a pdf attachment I made with mathematica to help try and explain my problem.

    please help if you can..


    Merlyn.
    I assume f(x) = \cos x ....?

    Then \int_0^{2 \pi} \cos^2 x \, dx = \int_0^{2 \pi} \frac{1}{2} [ \cos (2x) + 1] \, dx

    substituting from the usual double angle formula

     = \frac{1}{2} \int_0^{2 \pi} \cos (2x) + 1 \, dx = \pi.

    If you're studying Fourier Series it's expected you're familiar with basic techniques of integration.
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  3. #3
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    Quote Originally Posted by mercou View Post
    I have included a pdf attachment I made with mathematica to help try and explain my problem.

    please help if you can..


    Merlyn.
    Because of the symmetries of sinusoids the integral of \sin^2 or \cos^2 over a complete period is half of the area of the rectangle of height 1 and length equal to the period.

    Look at your diagram and you will see that this is obvious (draw a rectangle around the plot of \cos^2(x) from 0 to 2 \pi).

    Alternatively use the double angle formula to reduce the integral to one that can be done easily and by this tedious process you will arrive at the same result.

    CB
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