Explanation Given: The functions are y = − x 2 + 4 x − 3 , y = 0 , and axis y = − 1 . Formula used: Volume V = ∫ a b A ( x ) d x Where a ≤ x ≤ b and A = π [ ( Outer radius ) 2 − ( Inner radius ) 2 ] . Calculation: The functions are y = − x 2 + 4 x − 3 , y = 0 , and axis y = − 1 . The graphs of y = − x 2 + 4 x − 3 and y = 0 intersect where − x 2 + 4 x − 3 = 0 x 2 − 4 x + 3 = 0 Find the factors of the above equation. x 2 − 3 x − x + 3 = 0 x ( x − 3 ) − 1 ( x − 3 ) = 0 ( x − 1 ) ( x − 3 ) = 0 That is. ( x − 1 ) = 0 or ( x − 3 ) = 0 x = 1 or x = 3 The graph of the function is: Thus, the enclosed area lies over the interval [ 1 , 3 ] . Choose the slice of region bounded by the graphs y = − x 2 + 4 x − 3 vertically over the interval [ 1 , 3 ] . This vertical slice is perpendicular to the axis of rotation. Now, use the washer method to calculate the volume of the solid. For each x ∈ [ 1 , 3 ] , the washer with outer radius R = − x 2 + 4 x − 3 − ( − 1 ) = − x 2 + 4 x − 2 and inner radius r = 0 − ( − 1 ) = 1 . Now, find the volume...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 6, Problem 35CRE

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Find the volume of the solid obtained by rotating the region enclosed by the curves about the given axis.

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Chapter 6, Problem 34CRE

Chapter 6, Problem 36CRE

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Find the volume of the solid obtained by rotating the region enclosed by the curves y = 32 x2 y = 2 +1– x²| about - y = 25. (Use symbolic notation and fractions where needed.) Volume =| %3D

Use Washer Method to find the volume of the solid generated when the region enclosed by the given curves is rotated in its axis of revolution. a. x = 2y, y = 2 and y = 3; revolved about x-axis

Use any method to find the volume, V, of the solid obtained by rotating the region enclosed by the curves about the given axis. y² = x¯¹, x = 1, (Express numbers in exact form. Use symbolic notation and fractions where needed.) X = 6, axis y = −6 V = (156+24√√6 +ln(6))π Incorrect < Feedback You have not correctly calculated the volume of the solid. Slice the region vertically and use the washer method to find the volume of the solid of revolution. b [*(Router - Riner) dx a V = π X Note that a and b are the x-coordinates of the intersection points. Find Router as the distance from the axis of rotation to the top point of the region. Find Rinner as the distance from the axis of rotation to the bottom point of the region.

Chapter 6 Solutions

CALCULUS (CLOTH)

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

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Find the volume of the solid obtained by rotating the region enclosed by the curves about the given axis.

Solution Summary: The author calculates the volume of the solid obtained by rotating the region enclosed by the curves about the given axis.

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Find the volume of the solid obtained by rotating the region enclosed by the curves about the given axis.

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Chapter 6 Solutions