anonymous
  • anonymous
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 y-axis for y=x y=0 and x=2
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Zale101
  • Zale101
First, draw the graphs and identify the enclosed area. Have you done that already?
anonymous
  • anonymous
Yes
Zale101
  • Zale101
|dw:1434058993462:dw|

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Zale101
  • Zale101
Since we are revolving the shell around the y-axis, we will be using the example i circled. |dw:1434059042077:dw|
Zale101
  • Zale101
Makes sense?
anonymous
  • anonymous
yeah! except your axis kind of confuse me I thought the y and x were switched
anonymous
  • anonymous
But yeah I understand.
Zale101
  • Zale101
But before anything else. You will analyze the rectangle and see what function along the x-axis is higher and what functions where the x-axis is lower. |dw:1434059232453:dw|
anonymous
  • anonymous
ok I think I get it. The one thing im really confused on is the integral. do you use the numbers on the x-axis for the integral?
anonymous
  • anonymous
\[\int\limits_{0}^{3} 2\pi (x ^{2})\] so like this ?
anonymous
  • anonymous
i 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
  • Zale101
|dw:1434059661157:dw|
Zale101
  • Zale101
I forgot the mention, the intervals are based on where the spot is enclosed on the y-axis because we have dy and everything should be based on Y.
Zale101
  • Zale101
First step: Let's identify the intervals. What do you think the intervals are?
anonymous
  • anonymous
i gave you the wrong one by accident the problem says y=0 to x=3 so i think those are the intervals
anonymous
  • anonymous
i told you 2 but its 3 sorry about that
Zale101
  • Zale101
okay
Zale101
  • Zale101
So the intervals were right. But what did you get for the big x and the small x?
anonymous
  • anonymous
I don't know because the formula we learned dose not have that anywhere in there so i don't understand that.
anonymous
  • anonymous
I honestly thought i had it right and just wanted to double check my answers and make sure but now im super confused
Zale101
  • Zale101
\(\large a(x)=2\pi(radius)(height)\)
anonymous
  • anonymous
Yeah!
Zale101
  • Zale101
|dw:1434060538490:dw| \(\large a(x)=2pi(y)(X-x)\)
Zale101
  • Zale101
\[\Large \int\limits_{0}^{3}2 \pi y(X-x)dy\]
anonymous
  • anonymous
ok i still don't get the X-x 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
  • Zale101
|dw:1434060977099:dw| The radius is y, and the height is (X-x)
anonymous
  • anonymous
thanks for helping btw i know its a pain
Zale101
  • Zale101
|dw:1434061121877:dw| The big X is x=3 and the small x is y=x
Zale101
  • Zale101
Makes sense? Hope I didn't confused you...
anonymous
  • anonymous
ok yeah that makes sense.
anonymous
  • anonymous
ok! so then the next step is the anti derivative of that?
Zale101
  • Zale101
Yes.
Zale101
  • Zale101
Use the fundamental theorem of calculus to find the definite integral. \[\Large \int\limits_{a}^{b}f(y)dy=F(b)-F(a)\]
anonymous
  • anonymous
so 9pi or am i still not getting it?
anonymous
  • anonymous
omg! ok thank you so much!!
Zale101
  • Zale101
Np!
courtneygraley009
  • courtneygraley009
This calculator is designed to make the calculation of volumes easier without remembering the difficult formulas of volume. Try http://www.acalculator.com/volume-conversion-calculator.html

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