Consider the region bounded by y = x², y = 2x Write, but do not evaluate, an integral to find the volume of the solid whose base is the region an whose cross sections perpendicular to the x-axis are semicircles. 2 2 2 ㅠ 2x X S dx 2 7² ((2x)² – (2²¹)³²) da ㅠ 2π [ ²2 x (22 - 2² ) dx S² (2x − x²)² dx 2 S² (2x − x²) dr
Consider the region bounded by y = x², y = 2x Write, but do not evaluate, an integral to find the volume of the solid whose base is the region an whose cross sections perpendicular to the x-axis are semicircles. 2 2 2 ㅠ 2x X S dx 2 7² ((2x)² – (2²¹)³²) da ㅠ 2π [ ²2 x (22 - 2² ) dx S² (2x − x²)² dx 2 S² (2x − x²) dr
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...
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Transcribed Image Text:Consider the region bounded by y = x², y = 2x
Write, but do not evaluate, an integral to find the volume of the solid whose base is the region and
whose cross sections perpendicular to the x-axis are semicircles.
2
2
X
• L² = ( ² = 2² )' &
dx
0
2
7 S² ((2x)² – (x²)²) dz
2
2π
[² x (2x - x²) dx
2
2
[²
(2x - x²) ² dx
0
2
√² (2x − x²) da
-
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