Volume of Rotation

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Homework Statement



How do you find the volume of the solid obtained by rotating the region bounded by the given curves about the specified lines?

I keep getting a negative number and I"m becoming so frustrated! 11pi/30 is the answer in the textbook. Thank you so very much in advance!

Homework Equations



y=x^2
x=y^2
about y=1

The Attempt at a Solution



Area:
pi[(1-x^2)^2 - (1-x^(1/2))^2)]

Integral:
pi[1-2x^2+x^4-1+2x^(1/2)-x) between x=0 and x= 1

Antiderivative:
pi[(1/5x)^5-(2/3)x^3 + (2/3)x^(3/2)-(1/2)x^2]

Soln:
pi((2/10)-(5/10)) = -3pi/10???????
 
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Answers and Replies

  • #2
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I edited your post, removing most of the BBcode that you used. Physics Forums rules (https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/) discourage the overuse of special font styles in topics.
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When posting a new topic do not use the CAPS lock (all-CAPS), bold, oversized, non-standard, or brightly colored fonts, or any combination thereof. They are hard to read and are considered yelling. When replying in an existing topic it is fine to use CAPS or bold to highlight main points.
 
Last edited:
  • #3
36,038
7,972

Homework Statement



How do you find the volume of the solid obtained by rotating the region bounded by the given curves about the specified lines?

I keep getting a negative number and I"m becoming so frustrated! 11pi/30 is the answer in the textbook. Thank you so very much in advance!

Homework Equations



y=x^2
x=y^2
about y=1

The Attempt at a Solution



Area:
pi[(1-x^2)^2 - (1-x^(1/2))^2)]

Integral:
pi[1-2x^2+x^4-1+2x^(1/2)-x) between x=0 and x= 1

Antiderivative:

pi[(1/5x)^5-(2/3)x^3 + (2/3)x^(3/2)-(1/2)x^2]
You have a mistake in the line above. The coefficient 2/3 in the third term is wrong. I get what you reported to be the correct answer.
tree.lee said:
Soln:
pi((2/10)-(5/10)) = -3pi/10???????
 

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