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Q. 9

Expert-verifiedFound in: Page 1003

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.

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 $f(x,y)$ over a rectangular region defined in two directions x and y (say $a\le x\le b,c\le y\le d)$ 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 $.

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