Question

Show that the arclength of the curve y=(4-x^2/3)^3/2 for x=0 to x=8, as illustrated, is an improper integral and evaluate it.

Answer 1

arc length
\[\int\limits_0^8 \sqrt{1+(\frac{dy}{dx})^{2}} dx\]

Answer 2

\[\frac{dy}{dx} = -\frac{\sqrt{4-x^{2/3}}}{x^{1/3}}\]

Answer 3

i dont see how this becomes an improper integral?

Answer 4

The function we are integrating wouldn't be continuous at x=0 so the integral is improper.