Question

How do I find the riemann sum of `y = x^2 + 1` for [0,1] at infinitely small intervals?

Answer 1

Find a formula for the Riemann Sum with `n` equal intervals and then evaluate tha limit as `n rarr oo`.

The limit you are looking for is the integral, so find `int_0^1 (x^2 +1) dx`

So, if you have it available to you, use the Fundamental Theorem of Calculus:

`int_0^1 (x^2 +1) dx = 1/3x^3+x]_0^1`

`= (1/3 +1 ) - 0+0) = 4/3`