Turn rimen sum to integral

http://dl.dropbox.com/u/46294175/limitz.png


How do I do this question?

So I think b=1
and a =0
and b-a/n is 1 I think? But how do I keep going?

You are right about [a, b] = [0, 1], since then Δx = 1/n.

Next, a + jΔx = j/n <---> x, and thus f(x) = √(1 - x^2).

So, lim(n→∞) (1/n) Σ(j = 1 to n) √(1 - (j/n))^2
= ∫(x = 0 to 1) √(1 - x^2) dx
= Area of the first quadrant of the circle x^2 + y^2 = 1
= π/4.

I hope this helps!