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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- Jan 15th 2007, 04:20 PMJames234Differentiation 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 - Jan 15th 2007, 05:02 PMThePerfectHacker
What do you mean, "exists"?

Do you means the Riemann integral exists?

If that then yes it is true if $\displaystyle h(t)$ is continous.

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