Problem 1. Find the area of the shaded region in 7.3.61 y² = x(4 – x)². For this problem I am looking for the following: 1. Decide which approach is better for the task vertically (using dx) or horizontally (using dy)? Be sure to justify your answer. 2. Set up the definite integral to find the area of the enclosed loop.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
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I'm having a hard time setting up the integral for this one. Please help!

61. Finding Volumes of Solids Consider the graph of
y = x(4 – x)* (see figure). Find the volumes of the solids that
are generated when the loop of this graph is revolved about (a)
the r-axis, (b) the y-axis, and (c) the line x = 4.
= x(4 – x}=
3-
1 2 3As 61
Problem 1.
Find the area of the shaded region in 7.3.61 y? = x(4 – x)?. For this problem I am looking for the following:
1. Decide which approach is better for the task vertically (using dx) or horizontally (using dy)? Be sure to justify
your answer.
2. Set up the definite integral to find the area of the enclosed loop.
Transcribed Image Text:61. Finding Volumes of Solids Consider the graph of y = x(4 – x)* (see figure). Find the volumes of the solids that are generated when the loop of this graph is revolved about (a) the r-axis, (b) the y-axis, and (c) the line x = 4. = x(4 – x}= 3- 1 2 3As 61 Problem 1. Find the area of the shaded region in 7.3.61 y? = x(4 – x)?. For this problem I am looking for the following: 1. Decide which approach is better for the task vertically (using dx) or horizontally (using dy)? Be sure to justify your answer. 2. Set up the definite integral to find the area of the enclosed loop.
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