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anonymous
 one year ago
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the yaxis for
y=x y=0 and x=2
anonymous
 one year ago
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the yaxis for y=x y=0 and x=2

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Zale101
 one year ago
Best ResponseYou've already chosen the best response.1First, draw the graphs and identify the enclosed area. Have you done that already?

Zale101
 one year ago
Best ResponseYou've already chosen the best response.1Since we are revolving the shell around the yaxis, we will be using the example i circled. dw:1434059042077:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah! except your axis kind of confuse me I thought the y and x were switched

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But yeah I understand.

Zale101
 one year ago
Best ResponseYou've already chosen the best response.1But before anything else. You will analyze the rectangle and see what function along the xaxis is higher and what functions where the xaxis is lower. dw:1434059232453:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok I think I get it. The one thing im really confused on is the integral. do you use the numbers on the xaxis for the integral?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{3} 2\pi (x ^{2})\] so like this ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i used that and then plugged the integral in so i got \[18\pi \] as my answer is that right. I think we may have learned it a different way because we never used that Big X little x thing we use a set equation that combines circumference and height

Zale101
 one year ago
Best ResponseYou've already chosen the best response.1I forgot the mention, the intervals are based on where the spot is enclosed on the yaxis because we have dy and everything should be based on Y.

Zale101
 one year ago
Best ResponseYou've already chosen the best response.1First step: Let's identify the intervals. What do you think the intervals are?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i gave you the wrong one by accident the problem says y=0 to x=3 so i think those are the intervals

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i told you 2 but its 3 sorry about that

Zale101
 one year ago
Best ResponseYou've already chosen the best response.1So the intervals were right. But what did you get for the big x and the small x?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't know because the formula we learned dose not have that anywhere in there so i don't understand that.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I honestly thought i had it right and just wanted to double check my answers and make sure but now im super confused

Zale101
 one year ago
Best ResponseYou've already chosen the best response.1\(\large a(x)=2\pi(radius)(height)\)

Zale101
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434060538490:dw \(\large a(x)=2pi(y)(Xx)\)

Zale101
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large \int\limits_{0}^{3}2 \pi y(Xx)dy\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok i still don't get the Xx thing i thought it was just the equation which is in this case just x but then u times that by x from 2pi move the 2 pi out front because its a constant take the anti derivative of the x^2 so then you end up with \[2\pi \int\limits_{0}^{3} 1/3 x^{3}\]

Zale101
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434060977099:dw The radius is y, and the height is (Xx)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thanks for helping btw i know its a pain

Zale101
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434061121877:dw The big X is x=3 and the small x is y=x

Zale101
 one year ago
Best ResponseYou've already chosen the best response.1Makes sense? Hope I didn't confused you...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok yeah that makes sense.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok! so then the next step is the anti derivative of that?

Zale101
 one year ago
Best ResponseYou've already chosen the best response.1Use the fundamental theorem of calculus to find the definite integral. \[\Large \int\limits_{a}^{b}f(y)dy=F(b)F(a)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so 9pi or am i still not getting it?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0omg! ok thank you so much!!

courtneygraley009
 one year ago
Best ResponseYou've already chosen the best response.0This calculator is designed to make the calculation of volumes easier without remembering the difficult formulas of volume. Try http://www.acalculator.com/volumeconversioncalculator.html
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