Find the length of the following parametric curve
from the point (0,a) to the point (x,y).
I need to use the formula
but I'm not sure what the limits of integration are so I can evaluate the result.
As well, would be ? Or am I differentiating the ln incorrectly?
There is no "definite answer" because there is no definite question! You asked for the arclength from the specific point (0, a) to the variable point (x, y). Obviously the answer will depend upon (x,y). Since you are integrating with respect to t, NonCommAlg converted that to the variable , the value of t corresponding to (x,y).