Using differentiation, the slope of a curve can be found and using integration, the area under the curve is found.
How can calculus be used to determine the length of the curve represented by a given function?
If equation of trajectory of the proectile is given by y=f(x) which represents a parabola in a uniform gravitational field, I formulated the integral to find distance covered by the projectile as:

(R being the range)
I applied it in this question:
to find the total distance in order to find average speed.
However I did not get the right answer.
What changes need to be made in the integral?
What will be the integral used to find total distance in this question?