Volume of Solid: Find Y-Axis Rot. Region

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Homework Help Overview

The problem involves finding the volume of a solid formed by rotating a region defined by specific equations about the y-axis. The equations include an exponential function and boundaries along the x-axis.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to solve the problem by breaking it into parts, using both disk and washer methods. Some participants question the setup, particularly regarding the limits of integration and the orientation of the elements used for the volume calculation.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's approach. There is a focus on clarifying the correct method for rotation about the y-axis and ensuring the appropriate variables are used in the calculations.

Contextual Notes

Participants are discussing the implications of rotating around the y-axis versus the x-axis, which affects the choice of integration elements. There may be confusion regarding terminology related to volume elements.

africanmasks
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Homework Statement



Find the volume of the solid formed by rotating the region enclosed by the following equations about the Y-AXIS.

y= e^(3x)+5
y=0
x=0
x= 1/2

Homework Equations


The Attempt at a Solution



I keep getting the answer wrong. I broke the problem into two parts: solved a cylinder(disk) from y= 0 to 5 and solved a washer from y=5 to e^(3/2)+5

My answer was (1.25pi) (for cylinder or disk) + (.49811372pi) (for washer)
 
Last edited:
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Where's your work? For the cylinder wouldn't x go from 0 to 1/2?
 
you're rotating around the y not x
 
africanmasks said:
you're rotating around the y not x

Yes, so the cylinder elements are parallel to the y axis, sometimes called "dx elements". Your natural variable for that is x.

Maybe I misunderstand your terminology. Is what you call a cylinder what some texts call a shell?
 
Last edited:

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