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Thread: how can i solve the problem attached?

  1. #1
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    how can i solve the problem attached?

    Thank you in advance
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  2. #2
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    Re: how can i solve the problem attached?

    The integral is in $r$ which is also one of the limits.

    This is a no no. Do you have any idea what is intended?
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  3. #3
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    Re: how can i solve the problem attached?

    Changing the "dummy" variable to a different letter, x, this is \int_0^r xk_0\left(x\sqrt{\frac{s}{t}}\right)dx. Now, the obvious first substitution is y= x\sqrt{\frac{s}{t}} so x= y\sqrt{\frac{t}{s}} and dx= \sqrt{\frac{t}{s}}dy. When x= r y= r\sqrt{\frac{s}{t}}. The integral becomes \frac{t}{s}\int_0^{r\sqrt{\frac{s}{t}}} yk_0(y)dy. Now try a formula here: Bessel function of the first kind: Integration (subsection 21/01/02/01/01/01)
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