The Definite Integral: Quiz

Problem 6

Let Pn denote the partition of the interval [0, 2] into n subintervals of equal length. Let

f(x) = 4 – x

  1. What is the exact area of the region between x = 0 and x = 2, and bounded by f(x) and the x axis?
  2. What should n be so that U(Pn, f) is within 0.1 of this area?

Answers, problem 6

  1. The region is a trapezoid, so we can find its exact area = 1/2 * (2+4) * 2 = 6.
  2. 21, from the applet

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