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Home Integral The Definite Integral Problems
 
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Problems

Compute the following finite Riemann sums. If a hand calculator is available, the Riemann sums can also be computed with Δx = 1/10.

04_integration-82.gif 04_integration-83.gif
25

Let b be a positive real number and n a positive integer. Prove that if Δx = b/n,

04_integration-79.gif

Using the formula 04_integration-80.gif, prove that

04_integration-81.gif
26

Let H be a positive infinite hyperinteger and dx = b/H. Using the Transfer Principle and Problem 25, prove that04_integration-84.gifx dx = b2/2.
27

Let b be a positive real number, n a positive integer, and Δx = b/n. Using the formula

04_integration-85.gif

prove that

04_integration-86.gif
28 Use Problem 27 to show that 04_integration-87.gif x2 dx = b3/3.

Home Integral The Definite Integral Problems

Last Update: 2010-11-26