The region bounded by y = x and y = x² is rotated about the line x = 2. Which of the following would be the corresponding integral if we aim to obtain the volume of this object using the method of cylindrical =hells? О 2п 1 √ ² (2 + x)(x − x ²) da O 2π ○ 2π 1 (2 − x)(x − x²) dx 1 (2+x)(x − x²)² dx

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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The region bounded by y = x and y = x² is rotated about the line x = 2. Which of the following would
be the corresponding integral if we aim to obtain the volume of this object using the method of cylindrical
shells?
1
S₁²
О 2п
2πT
О 2п
1
•√²₁ (2 + x)(x − x ²) ² da
(2 + x)(x − x²) dx
O 2π
1
(2 − x)(x − x²) dx
-
1
+6² (2²
O 2π
(2+x)(2+x²) dx
1
= √ ² (²0
(x − 2)(x − x²) dx
Transcribed Image Text:The region bounded by y = x and y = x² is rotated about the line x = 2. Which of the following would be the corresponding integral if we aim to obtain the volume of this object using the method of cylindrical shells? 1 S₁² О 2п 2πT О 2п 1 •√²₁ (2 + x)(x − x ²) ² da (2 + x)(x − x²) dx O 2π 1 (2 − x)(x − x²) dx - 1 +6² (2² O 2π (2+x)(2+x²) dx 1 = √ ² (²0 (x − 2)(x − x²) dx
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