(a) Explanation Given information: Consider ℜ 1 is the region bounded by the curves y = x 2 , y = 0 and x = b . Consider ℜ 2 is the region bounded by the curves y = x 2 , x = 0 and y = b 2 . Calculation: Let ℜ 1 is the region below the graph of y = x 2 and above the x -axis between x = 0 and x = b . Let ℜ 2 is the region to the left of graph of x = y and to the right of the y axis between y = 0 and y = b 2 . Find the area region ℜ 1 bounded by the curves y = x 2 as shown below: A 1 = ∫ 0 b x 2 d x (1) Apply the integration in Equation (1): A 1 = [ 1 3 x 3 ] 0 b = b 3 3 Thus, the area of region ℜ 1 bounded by the curve is b 3 3 (b) To determine To find : the values of b such that ℜ 1 sweeps out the same volume when rotated about the x axis and y axis. (c) To determine To find : the values of b such that ℜ 1 sweeps out the same volume when rotated about the x axis. (d) To determine To find : the values of b such that ℜ 1 sweeps out the same volume when rotated about the y axis.

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Author: Stewart

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Chapter 6, Problem 35E

(a)

To determine

To find: the values of b such that the regions ℜ1 and ℜ1 have the same area.

(b)

To determine

To find: the values of b such that ℜ1 sweeps out the same volume when rotated about the x axis and y axis.

(c)

To determine

To find: the values of b such that ℜ1 sweeps out the same volume when rotated about the x axis.

(d)

To determine

To find: the values of b such that ℜ1 sweeps out the same volume when rotated about the y axis.

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Chapter 6, Problem 34E

Chapter 6, Problem 1PP

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Chapter 6 Solutions

CALCULUS,EARLY TRANS.-WEBASSIGN ACCESS

Ch. 6.1 - (a) Set up an integral for the area of the shaded...Ch. 6.1 - (a) Set up an integral for the area of the shaded...Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region. 5.Ch. 6.1 - Find the area of the shaded region. 6.Ch. 6.1 - Set up, but do not evaluate, an integral...Ch. 6.1 - Prob. 8E Ch. 6.1 - Set up, but do not evaluate, an integral...Ch. 6.1 - Set up, but do not evaluate, an integral...

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the values of b such that the regions ℜ 1 and ℜ 1 have the same area.

Solution Summary: The author explains that the values of b are underset_bne 0.

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To find: the values of b such that the regions ℜ1 and ℜ1 have the same area.

To find: the values of b such that ℜ1 sweeps out the same volume when rotated about the x axis and y axis.

To find: the values of b such that ℜ1 sweeps out the same volume when rotated about the x axis.

To find: the values of b such that ℜ1 sweeps out the same volume when rotated about the y axis.

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Chapter 6 Solutions