Calculus
Calculus
5th Edition
ISBN: 9781429241861
Author: Laura Taalman, Peter Kohn
Publisher: W. H. Freeman
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Chapter 4, Problem 1D
To determine

To give: the mathematical definition of Riemann sum of the function f over an interval

  [a,b].

Expert Solution & Answer
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Explanation of Solution

Given information:

Consider the function f over an interval [a,b].

Generally, the Riemann sum is the approximating the area under the curve.

  Calculus, Chapter 4, Problem 1D

Consider the function f is defined over an interval [a,b]. The interval is divided in to

n number of sub intervals with equal width Δx. .

Here, Δx=ban.

Here, xk is the kth end point of the subintervals. xk=a+kΔx

Then the Riemann sum

  abf(x)dx=k=1nf(xk*)Δx

Here, Δx=ban,xk=a+kΔx.

  xk* is the any sample point in the sub interval

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Chapter 4 Solutions

Calculus

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