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Expert-verified Found in: Page 1003 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # Discuss the similarities and differences between the definition of the definite integral found in Chapter 4 and the definition of the double integral found in this section.

Ans: Riemann sum is the basic requirement for evaluating the integral.

See the step by step solution

## Step 1. Given information:

definite integral and double integral.

## Step 2. Discussing the similarities and differences between the definition of the definite integral and double integral:

For a definite integral, equal to the limit of Riemann sum of a function of a single variable $f\left(x\right)$ over a closed interval (say [a, b]) as the number of subintervals goes to $\infty$.

Whereas, for a double integral, equal to the limit of a double Riemann sum of a function of two variables $f\left(x,y\right)$ over a rectangular region defined in two directions x and y (say $a\le x\le b,c\le y\le d\right)$ that has been subdivided into smaller subrectangles in both the x and y directions as the numbers of subintervals in those two directions goes to $\infty$. ### Want to see more solutions like these? 