Short Answer

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.

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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 $f (x)$ 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 $a \leq x \leq b, c \leq y \leq d)$ 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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Short Answer

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.

Step by Step Solution

Step 1. Given information:

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

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Calculus

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Short Answer

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.

Step by Step Solution

Step 1. Given information:

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

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