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Chapter 13: Q. 14 (page 1003)

Explain why using an iterated integral to evaluate a double integral is often easier than using the definition of the double integral to evaluate the integral.

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Most popular questions from this chapter

Evaluate the sums in Exercises $23 鈥� 28$ .

${鈭�}_{j = 1}^{3} {鈭�}_{k = 1}^{2} j^{k}$

Evaluate the sums in Exercises $23 鈥� 28$

${鈭�}_{i = 1}^{l} {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{m} i j^{2} k^{3}$

$L e t R = \{(x, y, z) | a_{1} 猢� x 猢� a_{2}, b_{1} 猢� y 猢� b_{2}, c_{1} 猢� z 猢� c_{2}\} . P r o v e t h a t : {鈭�}_{R} d V = (a_{2} - a_{1}) (b_{2} - b_{1}) (c_{2} - c_{1}) . W h a t i s t h e r e l a t i o n s h i p b e t w e e n R a n d t h e p r o d u c t (a_{2} - a_{1}) (b_{2} - b_{1}) (c_{2} - c_{1}) .$

Let $f (x, y, z)$ be a continuous function of three variables, let localid="1650352548375" $惟_{y z} = {(y, z) | a 鈮� y 鈮� b a n d h_{1} (y) 鈮� z 鈮� h_{2} (y)}$ be a set of points in the $y z$ -plane, and let localid="1650354983053" $惟 = {(x, y, z) | (y, z) 鈭� 惟_{y z} a n d g_{1} (y, z) 鈮� x 鈮� g_{2} (y, z)}$ be a set of points in $3$ -space. Find an iterated triple integral equal to the triple integral localid="1650353288865" $\underset{惟}{鈭�} f (x, y, z) d V$ . How would your answer change iflocalid="1650352747263" $惟_{y z} = {(y, z) | a 鈮� z 鈮� b a n d h_{1} (z) 鈮� x 鈮� h_{2} (z)}$ ?

Describe the three-dimensional region expressed in each iterated integral in Exercises 35鈥�44.

${鈭�}_{- 1}^{5} {鈭�}_{- 3}^{2} {鈭�}_{4}^{8} f (x, y, z) d z d x d y$

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91影视

Explain why using an iterated integral to evaluate a double integral is often easier than using the definition of the double integral to evaluate the integral.

Short Answer

Step by step solution

Step 1. Given information:

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