Help with solid of revolution volume question

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Homework Help Overview

The problem involves calculating the volume of a solid of revolution using the washer method. The original poster presents their setup for the integral, including the outer and inner radii, and the limits of integration.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to apply the washer method but questions the correctness of their outer radius and the resulting integral. Some participants question the definition of the outer radius and seek clarification on its value.

Discussion Status

Participants are actively discussing the setup of the problem, with some providing guidance on the definition of the outer radius. There is an ongoing exploration of the reasoning behind the values chosen for the radii, but no consensus has been reached regarding the original poster's approach.

Contextual Notes

The original poster's calculations yield an incorrect result, prompting questions about their assumptions and setup. The discussion includes a suggestion to visualize the problem graphically to aid understanding.

student93
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Homework Statement



The problem is attached in this post.

Homework Equations



The problem is attached in this post.

The Attempt at a Solution



I used washer method and set my outer radius as 2+2+√(x-1) and my inner radius as 2. I set my upper limit as 5 and my lower limit as 2.

I set my integral as π∫((4+√(x-1))^2-(4) dx, from 2 to 5 = 485π/6 which is incorrect, the actual answer is 157π/6.
 

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student93 said:
I used washer method and set my outer radius as 2+2+√(x-1)

Hi student93!

Why do you set the outer radius to 2+2+√(x-1)? Outer radius is simply 2+√(x-1), do you see why?
 
Could you please explain why that's the value of the outer radius? Also is the value of my inner radius correct?
 
student93 said:
Could you please explain why that's the value of the outer radius?
Draw a graph and select a disk, it becomes clear why the outer radius is that.
Also is the value of my inner radius correct?
Yes. :)
 

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