 
Summary: Math 3B Worksheet 2
G. Kennedy
Problem 1. Consider the function f(x) = 2x + 1.
1. Graph this function from x = 1 to 5.
2. Use one rectangle to estimate the area under this curve from 0 to 4. Call
this area R1.
3. Use a different rectangle to estimate the area under this curve from 0 to
4. Call this area R2.
4. Use 4 rectangles to estimate the area under this curve from 0 to 4. Call
this area R3.
5. Which is the more accurate measure of the area, R1, R2, or R3? Which
are overestimates? Which are underestimates?
6. Calculate
I =
4
0
f(x)dx.
7. Calculate the differences between I and R1, I and R2, and I and R3.
8. Were your answers to part 5 correct?
1
