Approximating the area under a curve

Using rectangles to approximate the area under a curve practice problems.

Problem

Let A denote the area of the shaded region shown below.
We can approximate the exact area A using the following Riemann sums.
L, left parenthesis, 2, right parenthesis is the left-hand rule with 2 equal subdivisions.
R, left parenthesis, 2, right parenthesis is the right-hand rule with 2 equal subdivisions.
L, left parenthesis, 5, right parenthesis is the left-hand rule with 5 equal subdivisions.
M, left parenthesis, 5, right parenthesis is the midpoint rule with 5 equal subdivisions.
R, left parenthesis, 5, right parenthesis is the right-hand rule with 5 equal subdivisions.
Put these five approximations in order from smallest to largest.
  • L, left parenthesis, 2, right parenthesis
  • R, left parenthesis, 2, right parenthesis
  • M, left parenthesis, 5, right parenthesis
  • R, left parenthesis, 5, right parenthesis
  • L, left parenthesis, 5, right parenthesis