
Improper Integral Help
I am just starting on the improper integral section. I am having trouble with this problem because I cannot seem to break it down easily into something that does not have (x5) in the denominator. If I try to do lim R > 5+, I will still get an undefined answer. I am doing something wrong, but I do not know what.
12. $\displaystyle \int^6_5 \frac{dx}{(x5)^{3/2}}$
I get the general antiderivative, but I cannot get rid of the denominator, and since the numerator is just 1, I cannot use L'Hopital's Rule. :(
Thanks for your help.

Using the substitution $\displaystyle t=x5$
$\displaystyle \displaystyle\int_5^6\dfrac{dx}{(x5)^{3/2}}=\displaystyle\int_0^1\dfrac{dt}{t^{3/2}}=\displaystyle\lim_{ \epsilon \to 0^+}{\displaystyle\int_{\epsilon}^{ 1}\dfrac{dt}{t^{3/2}}}=\displaystyle\lim_{ \epsilon \to 0^+}\left[\dfrac{2}{\sqrt{t}}\right]_{\epsilon}^1=\ldots$


Quote:
Originally Posted by
Warrenx Thank you very much!
You are welcome!