PLEASE HELP ME CALCULUS CYLINDRICAL SHELLS

Calculus
Tutor: None Selected Time limit: 1 Day

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.

y = 5
x
,      y = 0,     x = 1;     about x = −4
Jul 30th, 2015

Thank you for the opportunity to help you with your question!

nteresting, usually the method of cylindrical shells is used when finding the volume of the solid obtained by rotating about y-axis. 

Vy = 2pi*[a;b] ∫ x*f(x) dx 

Bur I suppose that it can be used analogically about x-axis 

Vx = 2pi*[c;d] ∫ y*g(y) dy 

Given function is 125y = x^3 -----> x = (125y)^1/3 = 5*y^1/3. 

Then 
Vx = 2pi*[0; 8] ∫ y* 5*y^1/3 dy = 10pi * [0; 8] ∫ y^4/3 dy = 

= 10pi *3/7 * y^7/3 [0; 8] = 30pi/7 * 8^7/3 = 30pi/7 * 2^7 = 

=30pi/7 *128 = 3840pi/7

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 30th, 2015

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Jul 30th, 2015
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Jul 30th, 2015
Dec 7th, 2016
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