Given f(x) = x^2 + 3 find the area A of the region under f(x) on the interval [1, 3]?

Question

by first computing
n
∑ f(x) ∆x and then taking the limit as n→∞
i=1

Answer 1

So, just do it, start with n=2 because there are only 2 rectangles under the curve between 1 and 3.

(1^2 + 3)*1 + (2^2+3)*1 = 11

As n->infinity it is unlimited. I'm not sure that is really what is is asking. It should be asking as delta x goes to 0. You want to integrate between 1 and 3. You end up with:

(x^3)/3 + 3x

= (9 + 9) - (1/3 + 3) = 14 2/3

Answer 2

solving the integral you get
x^3/3+3x
evaluating it in 3 and 1
you get 44/3