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Definite Integrals

Definite Integrals

Midpoint Sum Exercises

Example 1

Let f(x) = sin(x) + 1. Use a midpoint sum with 2 equal sub-intervals to estimate the area between f and the x-axis on [0, 2π].

Example 2

Let g(x) = x3 on the interval [0, 12]. Use a midpoint sum with 4 equal sub-intervals to estimate the area between g and the x-axis on this interval.

Example 3

Partial values of the function h are given in the table below. Use a midpoint sum with 3 intervals to estimate the area between h and the x-axis on [-2, 4] or explain why you can't. 

Example 4

Partial values of the function f(x) are given in the table below. Use a midpoint sum with 4 equal sub-intervals to estimate the area between f and the x-axis on [0, 1], or explain why you can't.