© 2014 Shmoop University, Inc. All rights reserved.
Definite Integrals

Definite Integrals

Example 1

Let f (x) = x2. Calculate the following quantities.

  • (f (12)-f (0))(12)
  • (f (12)-f (0))(6)
  • (f (12)-f (0))(4)
  • (f (12)-f (0))(3)
  • (f (12)-f (0))(1)

Example 2

Let f (x) = x2 on the interval [0,12]. How many rectangles must we use to guarantee that the right- and left-hand sums are within 10 of each other?

Example 3

Let f (x) = 4x + 6 on the interval [2,8]. How many rectangles must we use to ensure that the left-hand sum is within 0.25 of the exact area between f and the x-axis on this interval?

Example 4

Let f (x) = x4 on the interval [-2,-1]. For what values of n are LHS(n) and RHS(n) within 0.5 of each other on this interval?

Example 5

Let f (x) = cos(x) on the interval  How large must n be to guarantee that LHS(n) is within 0.3 of the exact area between f and the x-axis on this interval?

Advertisement
Advertisement
Advertisement