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Math Calculus Calculus - Standalone book

Which of the integrands (i)–(iv) is used to compute the volume obtained by rotating region R about y = − 2 in the figure. i. ( f ( x ) 2 + 2 2 ) − ( g ( x ) 2 + 2 2 ) ii. ( f ( x ) + 2 ) 2 − ( g ( x ) + 2 ) 2 iii. ( f ( x ) 2 − 2 2 ) − ( g ( x ) 2 − 2 2 ) iv. ( f ( x ) − 2 ) 2 − ( g ( x ) − 2 ) 2

Which of the integrands (i)–(iv) is used to compute the volume obtained by rotating region R about y = − 2 in the figure. i. ( f ( x ) 2 + 2 2 ) − ( g ( x ) 2 + 2 2 ) ii. ( f ( x ) + 2 ) 2 − ( g ( x ) + 2 ) 2 iii. ( f ( x ) 2 − 2 2 ) − ( g ( x ) 2 − 2 2 ) iv. ( f ( x ) − 2 ) 2 − ( g ( x ) − 2 ) 2

Solution Summary: The author explains which of the integrands (i)–(iv) is used to compute the volume obtained by rotating region R about y = 2.

Calculus - Standalone book

Calculus - Standalone book

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.3, Problem 13E

To determine

Which of the integrands (i)–(iv) is used to compute the volume obtained by rotating region R about $y = - 2$ in the figure.

i. $(f {(x)}^{2} + 2^{2}) - (g {(x)}^{2} + 2^{2})$

ii. ${(f (x) + 2)}^{2} - {(g (x) + 2)}^{2}$

iii. $(f {(x)}^{2} - 2^{2}) - (g {(x)}^{2} - 2^{2})$

iv. ${(f (x) - 2)}^{2} - {(g (x) - 2)}^{2}$

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Chapter 6.3, Problem 12E

Chapter 6.3, Problem 14E

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Let a and b two real numbers such that a < b. A region R is bounded by a curve C and two different lines parallel to the r-axis. Please note that C does cut the y-axis in the interval [a, b. The volume V of the solid generated by rotating R about the y-axis can be expressed as V = c Bdu, where 1 (1) c = -; T (2) c = VT; (3) c = T; (4) c = 72: (5) The two lines are x = a, y = b; (6) The two lines are y = a; x = b; (7) The two lines are x = a, x = b; (8) The two lines are y = a, y = b; (9) B = f(x), where f is a function of x; (10) B = g(y), where g is a function y; (11) d = 1; (12) d = 2: 1 (13) d = 21 (14) u = 1; (15) u = 2;

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Chapter 6 Solutions

Calculus - Standalone book

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