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Math Help - Differentiation and Integral

  1. #1
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    Differentiation and Integral

    It's similar to something I posted before but how would I show that
    the integral from 0 to x of h(t)sin(x-t)dt exists?

    I'm sure it's similar but the same with
    the integral from 0 to x of h(t)cos(x-t)dt
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  2. #2
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    Quote Originally Posted by James234 View Post
    It's similar to something I posted before but how would I show that
    the integral from 0 to x of h(t)sin(x-t)dt exists?
    What do you mean, "exists"?

    Do you means the Riemann integral exists?
    If that then yes it is true if h(t) is continous.

    Thus, since \sin (x-t) is continous and h(t) is continous thus is their product. And hence any continous function is Riemann integratable.
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