(e) It is possible to compute the volume of a solid of revolution using disk/washer method if and only if it is also possible to compute the volume of the solid using shell method.

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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I need help on this question for letter (e) please. If it's true, can you prove it and if it's false, can you show me how I can provide a counterexample please? Show full work please. Thank you in advance. 

1. Label each of the following statements as true or false. If true, prove statement. If false,
provide a counterexample. If a proof or counterexample is not provided, you will receive 0
points for the exercise.
(a) Let f and F be functions such that F' = f. Then f(x)dx = F(b) – F(a). (Hint: read
the statement carefully!)
(b) Suppose a curve C is parameterized using parameter t. Suppose also that y(t) 2 0 for
t€ [a,b). Then * y(t)dx > 0.
(c) A solid may have finite volume but infinite surface area.
(d) Let p, (2) be an nth degree polynomial. Then S Pa(x) In(x)dx may be integrated using
integration by parts n times.
(e) It is possible to compute the volume of a solid of revolution using disk/washer method if
and only if it is also possible to compute the volume of the solid using shell method.
Transcribed Image Text:1. Label each of the following statements as true or false. If true, prove statement. If false, provide a counterexample. If a proof or counterexample is not provided, you will receive 0 points for the exercise. (a) Let f and F be functions such that F' = f. Then f(x)dx = F(b) – F(a). (Hint: read the statement carefully!) (b) Suppose a curve C is parameterized using parameter t. Suppose also that y(t) 2 0 for t€ [a,b). Then * y(t)dx > 0. (c) A solid may have finite volume but infinite surface area. (d) Let p, (2) be an nth degree polynomial. Then S Pa(x) In(x)dx may be integrated using integration by parts n times. (e) It is possible to compute the volume of a solid of revolution using disk/washer method if and only if it is also possible to compute the volume of the solid using shell method.
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