You don't need parametrization. You can write it as 2 functions: and .
Note that this function is same when reflected about x-axis, so you can find arc length of and then just double result.
I'm trying to find the arc length of (x^3)(y^2) = 1 from (1,1) to (9,1/27). I tried parameterizing the function as r(t) = (t,t^-3/2) with no luck. I can't seem to find a way to evaluate the integral using u-substitution or trig sub. Any ideas? Thanks.
You don't need parametrization. You can write it as 2 functions: and .
Note that this function is same when reflected about x-axis, so you can find arc length of and then just double result.
It looks like the original poster is only trying to find the length of a portion of the upper arc. Notice that he wanted the arc length between the points and .
Finding the arc length of leads to the integral , which cannot be evaluated in terms of elementary functions. Hence the poster's question.
We can find a numeric solution, however. The length appears to be approximately 8.2373.
Thanks for confirming my suspicions. I think perhaps the instructor made a typo on the assignment. I tried all sorts of crazy stuff like a trig substitution that led to a integration by parts. It just didn't seem like it was leading anywhere, except maybe driving me crazy lol.