Explanation Given data: x = t ( 1 − t ) (1) y = 1 + t 2 (2) Calculation: Since the graph bound about the y -axis, substitute 0 for x in equation (1) as follows. t ( 1 − t ) = 0 1 − t = 0 t = 1 Substitute 1 for t in equation (2) as follows. y = 1 + 1 2 = 1 + 1 = 2 Consider the expression to obtain the volume swept out by revolving region bounded by y -axis with a graph of x = t ( 1 − t ) , y = 1 + t 2 . Volume = ∫ 1 2 π x 2 d y Substitute t ( 1 − t ) for x as follows. Volume = ∫ 0 1 π [ t ( 1 − t ) ] 2 2 d t { ∵ d y = 2 d t }

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Chapter 10.2, Problem 50E

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Calculate the volume swept out by revolving region bounded by y-axis with a graph of x=t(1−t), y=1+t2.

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Chapter 10.2, Problem 49E

Chapter 10.2, Problem 51E

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Calculate the volume swept out by revolving region bounded by y-axis with a graph of x=t(1−t), y=1+t2.

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Chapter 10 Solutions