How do you calculate the derivative of #[int(sqrt(1+(dy/dx)^2)/60 dx)]#?
Notice how the integral is the opposite of a derivative. The first part of the Fundamental Theorem of Calculus states that, and the term "antiderivative" essentially describes the basic function of an integral. Therefore, the derivative of an integral is the integrand. In other words:
(yes, the indefinite integral of zero is a constant)
For this, we would be using the upper case, differentiating an integral.
We start with:
which, by the way, is the equation for 1/60th times an arc length over an interval
If we were to try to evaluate this integral manually, even with something like