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Thread: Integral/Cos problems

  1. #1
    kym
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    Integral/Cos problems

    Integral/Cos problems-1.pngIntegral/Cos problems-2.png
    I don't understand why the integral of cos in both pictures is equal to 0. Also in the second picture both cos suffered a transformation in the second step(t1 became t1+t2 etc...).
    Could someone explain why this happens? I'm trying to understand but without success.
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  2. #2
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    Re: Integral/Cos problems

    The integral of any sinusoid over an integer multiple of a full period will be zero.

    Think about it, you have two identical portions of opposite signs.
    Integration results in adding these portions which cancel each other out.

    I can't make heads or tails of the second picture but you can do whatever you like to the argument
    and as long as you integrate over a integer number of periods the result will be zero.
    Thanks from kym
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  3. #3
    kym
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    Re: Integral/Cos problems

    Ok thanks, I understand it more or less now but that integral of a cos with (t1-t2) as argument in the second picture shouldn't be 0 aswell? That is confusing me a bit.
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    Re: Integral/Cos problems

    Quote Originally Posted by kym View Post
    Ok thanks, I understand it more or less now but that integral of a cos with (t1-t2) as argument in the second picture shouldn't be 0 aswell? That is confusing me a bit.
    Ok I looked more carefully at this.

    The answer is no because the 2nd term is independent of $\theta$

    So integrating over $0$ to $2\pi$ just ends up multiplying the integrand by $2\pi$
    Thanks from kym
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