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Thread: Prove this integral is equal to zero

  1. #1
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    Prove this integral is equal to zero

    I was tutoring an engineer student and we are stuck at this one problem.

    Prove that $\displaystyle \frac {1}{T} \int _{0}^{T} [V I \sin ( \theta ) \sin (2 \omega t ) ] dt = 0$

    I rarely deal with integrals like this and not really sure how to proceed. He is taking an undergrad. engineering class and I suppose this shouldn't be too difficult. Are there any hints or at least some resource I can read get hints from?

    Thank you.
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    I was tutoring an engineer student and we are stuck at this one problem.

    Prove that $\displaystyle \frac {1}{T} \int _{0}^{T} [V I \sin ( \theta ) \sin (2 \omega t ) ] dt = 0$

    I rarely deal with integrals like this and not really sure how to proceed. He is taking an undergrad. engineering class and I suppose this shouldn't be too difficult. Are there any hints or at least some resource I can read get hints from?

    Thank you.
    Is $\displaystyle \omega$ defined in terms of $\displaystyle T$?
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    Quote Originally Posted by tttcomrader View Post
    I was tutoring an engineer student and we are stuck at this one problem.

    Prove that $\displaystyle \frac {1}{T} \int _{0}^{T} [V I \sin ( \theta ) \sin (2 \omega t ) ] dt = 0$

    I rarely deal with integrals like this and not really sure how to proceed. He is taking an undergrad. engineering class and I suppose this shouldn't be too difficult. Are there any hints or at least some resource I can read get hints from?

    Thank you.
    What's that $\displaystyle \theta$ doing in there? You could start by taking the $\displaystyle VI$ out and if $\displaystyle \theta$ is suppose to be there then that's constant so take that one out too. Otherwise, why don't you just evaluate the general expression:

    $\displaystyle \int_0^T \sin(t)\sin(2\omega t)dt=0$

    and figure out what $\displaystyle T,\omega$ have to be to make it so.
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