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Definite Integrals

Definite Integrals

Midpoint Sum Examples

Example 1

Use a midpoint sum with 2 sub-intervals to estimate the area between the function f(x) = x2 + 1 and the x-axis on the interval [0, 4].

Example 2

Partial values of the function g are given in the table below.

  • Use a midpoint sum with three sub-intervals to estimate the area between the graph of g and the x-axis on [0, 12].
  • Could we use this table to take a midpoint sum with 4 equal sub-intervals? Why or why not?
  • Could we use this table to take a midpoint sum with 6 equal sub-intervals? Why or why not?

Example 3

A graph of the function h is shown below. Use a midpoint sum with 3 sub-intervals to estimate the area between the graph of h and the x-axis on [0, 3].

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