Are you supposed to obtain the limit of the Riemann sum OR integrate?
And n goes to infinity not x.
The following sum
is a right Riemann sum for the definite integral where = ? = 3
and = ? = sqrt(9-x^2)
The part of the question I'm stuck on is:
The limit of these Riemann sums as is = ?
I know that I need to evaluate:
lim(n->inf) sum from 0 to n of sqrt(9-(3i/n)^2) but after scaring the 3i/n part, I'm stuck.
Any help would be GREATLY appreciated!
Thanks in advance!
P.S.
Does this whole question involve a topic called "Riemann sums?"
Well, the whole point is that since that sum is a Riemann sum for the integral its limit as n goes to infinity must be the integral!
And you don't even have to do an integral. If , then except that - the upper half of a circle of radius 3 with center at the origin. And since the integral is from x= 0 to x= 3 rather than -3 to 3, that integral is the area of 1/4 of a circle of radius 3.