1. You are going to investigate left, midpoint, and right Riemann sums using Geogebra
2. Investigate several aspects of using rectangles to approximate areas under curves.

Investigate the area under the following curves:
1. f(x) = x^2 +1 between [0,2]
2. f(x) = x^3 between [1,3] using 2, 4, and 6 rectangles & make a conclusion about the approximations
3. A scientist wants to estimate the area between the x-axis and the graph of
y = x3 −9x2 +15x + 30 for −1≤ x ≤ 7 . For safety reasons she wants to underestimate the area.
She decides to use left-side and right-side Riemann sums to make the estimate. On what subinterval(
s) should she use the left-side sums and on what interval(s) should she use the right-sides
sums? Justify your answer.