To show that the solid obtained by rotating the region R about the y -axis has volume V = 2 π ( 1 − c ) where c = f ( a ) , by using the Shell Method and the substitution u = f ( x ) . Also observe that as c → 0 , the region R becomes infinite but the volume approaches 2 π

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Answer 1

Question

Chapter 6.4, Problem 64E

To determine

To show that the solid obtained by rotating the region $R$ about the $y$ -axis has volume $V = 2 π (1 - c)$ where $c = f (a)$ , by using the Shell Method and the substitution $u = f (x)$ . Also observe that as $c \to 0$ , the region $R$ becomes infinite but the volume approaches $2 π$

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4. Use method of separation of variable to solve the following wave equation მłu J²u subject to u(0,t) =0, for t> 0, u(л,t) = 0, for t> 0, = t> 0, at² ax²' u(x, 0) = 0, 0.01 x, ut(x, 0) = Π 0.01 (π-x), 0

Answer 2

Question

Chapter 6.4, Problem 64E

To determine

To show that the solid obtained by rotating the region $R$ about the $y$ -axis has volume $V = 2 π (1 - c)$ where $c = f (a)$ , by using the Shell Method and the substitution $u = f (x)$ . Also observe that as $c \to 0$ , the region $R$ becomes infinite but the volume approaches $2 π$

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Answer 3

Question

Chapter 6.4, Problem 64E

To determine

To show that the solid obtained by rotating the region $R$ about the $y$ -axis has volume $V = 2 π (1 - c)$ where $c = f (a)$ , by using the Shell Method and the substitution $u = f (x)$ . Also observe that as $c \to 0$ , the region $R$ becomes infinite but the volume approaches $2 π$

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Answer 4

Question

Chapter 6.4, Problem 64E

To determine

To show that the solid obtained by rotating the region $R$ about the $y$ -axis has volume $V = 2 π (1 - c)$ where $c = f (a)$ , by using the Shell Method and the substitution $u = f (x)$ . Also observe that as $c \to 0$ , the region $R$ becomes infinite but the volume approaches $2 π$

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Answer 5

Chapter 6.4, Problem 64E

To determine

To show that the solid obtained by rotating the region $R$ about the $y$ -axis has volume $V = 2 π (1 - c)$ where $c = f (a)$ , by using the Shell Method and the substitution $u = f (x)$ . Also observe that as $c \to 0$ , the region $R$ becomes infinite but the volume approaches $2 π$

Answer 6

Chapter 6.4, Problem 64E

To determine

To show that the solid obtained by rotating the region $R$ about the $y$ -axis has volume $V = 2 π (1 - c)$ where $c = f (a)$ , by using the Shell Method and the substitution $u = f (x)$ . Also observe that as $c \to 0$ , the region $R$ becomes infinite but the volume approaches $2 π$

Answer 7

Chapter 6.4, Problem 64E

To determine

To show that the solid obtained by rotating the region $R$ about the $y$ -axis has volume $V = 2 π (1 - c)$ where $c = f (a)$ , by using the Shell Method and the substitution $u = f (x)$ . Also observe that as $c \to 0$ , the region $R$ becomes infinite but the volume approaches $2 π$

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

To show that the solid obtained by rotating the region R about the y -axis has volume V = 2 π ( 1 − c ) where c = f ( a ) , by using the Shell Method and the substitution u = f ( x ) . Also observe that as c → 0 , the region R becomes infinite but the volume approaches 2 π

Solution Summary: The author proves that the solid obtained by rotating the region R about the y -axis has volume V = 2 ( 1

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To show that the solid obtained by rotating the region $R$ about the $y$ -axis has volume $V = 2 π (1 - c)$ where $c = f (a)$ , by using the Shell Method and the substitution $u = f (x)$ . Also observe that as $c \to 0$ , the region $R$ becomes infinite but the volume approaches $2 π$

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Chapter 6 Solutions

To show that the solid obtained by rotating the region R about the y -axis has volume V = 2 π ( 1 − c ) where c = f ( a ) , by using the Shell Method and the substitution u = f ( x ) . Also observe that as c → 0 , the region R becomes infinite but the volume approaches 2 π

Solution Summary: The author proves that the solid obtained by rotating the region R about the y -axis has volume V = 2 ( 1

Concept explainers

Videos