Calculus 1- Question Involving Riemann Sums

Question

Use Riemann sums and limits to find the area under the given function on the given interval.

f(x) = x+1, [0,2]

Answer 1

Area under the line and above the x axis is a rectangle 2 by 1 plus a triangular area = 1/2 of 2 by 2 or

2+2 = 4

f(x) =x+1, integrate to get F(x) = x^2/2 + x, evaluate at x=2: (2)^2/2 +2 = 2+2 = 4

Or break up the interval into 2 intervals, each with base = 1, midpoint of each interval is 1/2 and 3/2

f(1/2) = 1/2 +1 = 3/2

f(3/2) = 3/2 + 1 = 5/2

3/2 + 5/2 = 8/2 = 4 = Area