Let R be the region bounded by the graphs of y = x + 3, y = x3 + 1 and the lines x = 1 and y = 0 as shown. SET UP the definite integral for the volume of the solid generated when R is: i. revolved about x = 2 (using disks and/or washers). ii. revolved about y = −1

Let R be the region bounded by the graphs of y = x + 3, y = x3 + 1 and the lines x = 1 and y = 0 as shown. SET UP the definite integral for the volume of the solid generated when R is: i. revolved about x = 2 (using disks and/or washers). ii. revolved about y = −1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.3: Algebraic Expressions

Problem 20E

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Question

Let R be the region bounded by the graphs of y = x + 3, y = x³ + 1 and the lines x = 1 and y = 0 as shown.

SET UP the definite integral for the volume of the solid generated when R is:
i. revolved about x = 2 (using disks and/or washers).
ii. revolved about y = −1 (using cylindrical shells)

• (1, 4)
x = 1
y = x + 3
(1,2)
y = x³ +1
R
(-3, 0)
(-1,0)

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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