Unam
Find the volume of the solid obtained by rotating the region bounded by
x=8 y^2, y = 1, x = 0, about the y-axis.
a) 8 y^2=0, x=0, how can I solve this when its like this, I mean there's no other x values so i can use the (0, ?)∫.
I'm using this V = π ∫ f(x)² dx {a,b}
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Unam
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|dw:1351976086595:dw|
klimenkov
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|dw:1351976458012:dw|
Unam
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What's the graph between? 0 to 8 or 0 to 1?
klimenkov
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You can't use this formula in this case.
Unam
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oh ok...
klimenkov
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|dw:1351976777364:dw|
And now you can. Calculate this integral and it will be the volume.
Unam
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thanks so down we... v= π (0,1) ∫(8x^2)^2 dx-(8-x)^2π?
Unam
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don't*
klimenkov
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Can't understand you, just calculate the integral I've written. And it will be the volume. Can you do this?
Unam
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sorry, yup i can
klimenkov
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You can type the result and I will check it.
Unam
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ok :)
Unam
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64π/5?
klimenkov
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Yes. That's correct.
Unam
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Oh thanks so much!
Unam
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so I just use 1 and 0 for ∫?
Unam
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|dw:1351977717019:dw|
Unam
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i know how i get 0 but not sure about 1, we use the graph right? cos its not between 0 and 1?
klimenkov
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You need to understand how the formula is built to get how to solve this problem. I just switch x and y, so you can use your formula.
Unam
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Ah ok
klimenkov
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If you will rotate the area on my second figure about x-axes you will get the volume i drew on the first figure. Got it?
Unam
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YEs!!!
Unam
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thanks much Klim!!
klimenkov
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No problems.