Chapter 13 Double and Triple Integrals 1004 exy dA, 18. where R = {(x, y) | 1 < x < 2 and 1 < y < 3} 13. State Fubini's theorem. 14. Explain why using an iterated integral to evaluate a dou- ble integral is often easier than using the definition of the double integral to evaluate the integral. / cos(xy) dA, R. 19. 15. Explain how the Fundamental Theorem of Calculus is used in evaluating the iterated integral S f(x, y) dy dx. {(+,y) 1 x드플 and 드y 드지 where R = 2 16. Explain how the Fundamental Theorem of Calculus is 20. Use the results of Exercises 18 and 19 to explain why 't 2 may not be possible to evaluate a double integral by us- used in evaluating the iterated integral " S"f(x, y) dx dy. 17. Earlier in this section, we showed that we could use Fubini's theorem to evaluate the integral lex²y dA and 21. Show that Sa Se f(x, y) dy dx does not always equal Sa Sa f(x, y) dx dy by evaluating these two iterated inte- we showed that x?y dx dy = 91. Now evaluate when a = c = 0 and b = d = 1 grals for f(x, y) = Why does this result not violate Fubini's theorem? 22. Outline the steps required to find the volhume solid bounded by the graph of a function f(x, v) an Noxy-plane for a < x
Chapter 13 Double and Triple Integrals 1004 exy dA, 18. where R = {(x, y) | 1 < x < 2 and 1 < y < 3} 13. State Fubini's theorem. 14. Explain why using an iterated integral to evaluate a dou- ble integral is often easier than using the definition of the double integral to evaluate the integral. / cos(xy) dA, R. 19. 15. Explain how the Fundamental Theorem of Calculus is used in evaluating the iterated integral S f(x, y) dy dx. {(+,y) 1 x드플 and 드y 드지 where R = 2 16. Explain how the Fundamental Theorem of Calculus is 20. Use the results of Exercises 18 and 19 to explain why 't 2 may not be possible to evaluate a double integral by us- used in evaluating the iterated integral " S"f(x, y) dx dy. 17. Earlier in this section, we showed that we could use Fubini's theorem to evaluate the integral lex²y dA and 21. Show that Sa Se f(x, y) dy dx does not always equal Sa Sa f(x, y) dx dy by evaluating these two iterated inte- we showed that x?y dx dy = 91. Now evaluate when a = c = 0 and b = d = 1 grals for f(x, y) = Why does this result not violate Fubini's theorem? 22. Outline the steps required to find the volhume solid bounded by the graph of a function f(x, v) an Noxy-plane for a < x
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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