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anonymous
 5 years ago
Find the volume of a solid generated by revolving the graphs of the functions y=62xx^2 and y=x+6 about the line y=2
Intersections points are x=3 and x=0
I think the radius of the solid should be 62xx^2(x+6)2 which is 23xx^2
then I have Vol = pi*Integral from 3 to 0 of (23xx^2)^2dx
I integrate and get pi *[4x65/5+3/2x^4+13x^3/3+6x^2+4x ] evalulated between 3 and 0. I end up with 147.9pi which seems way too big.Can you find my mistake? Thank you so much!!!
anonymous
 5 years ago
Find the volume of a solid generated by revolving the graphs of the functions y=62xx^2 and y=x+6 about the line y=2 Intersections points are x=3 and x=0 I think the radius of the solid should be 62xx^2(x+6)2 which is 23xx^2 then I have Vol = pi*Integral from 3 to 0 of (23xx^2)^2dx I integrate and get pi *[4x65/5+3/2x^4+13x^3/3+6x^2+4x ] evalulated between 3 and 0. I end up with 147.9pi which seems way too big.Can you find my mistake? Thank you so much!!!

This Question is Closed

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1if i see it right; you went ahead and subtracted 2 to get it to the x axis right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1y = 4 2x x^2 y = x+4 and spin that around the x axis (y=0)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1is your interval good? 62xx^2 x6 x^2 3x = 0 x(x+3) = 0; x= [3,0] is good

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Since it is being revolved around y=2, I was subtracting 2 to eliminate that much verticasl distance from the radius.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1then we can integrate: subtract one function from the other... 42xx^2  x4 pi [S] [x^3 3x]^2 dx ; [3,0]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1pi [S] (x^6 +9x^2 +6x^4) dx right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.123xx^2 is your function; why?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1it doesnt match my radius tho :) so whos right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1y=62xx^2 (2) = 42x x^2 y=x+6 (2) = x+4

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.14 2x x^2 [x+4] 3x x^2 right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so I need to subtact 2 from both functions?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1Yes, becasue you need to move both function pi [S] (x^6 +9x^2 +6x^4) dx pi (x^7/7 +3x^3 + 6x^5/5) ; [3,0]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0How are you getting thisx^6 +9x^2 +6x^4) dx

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1you gotta squre your radius

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1[f(x)]^2 = [2xx^2]^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If the radius is (3xx^2) and we square it, don't we get 9x^26x^3=x^4?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.13x(3x) = 9x^2 x^2(x^2) = x^4 3x(x^2)(2) = +6x^3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1we could go with 1(3x+x^2) as well i htink

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1but then we get  everything

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That 's OK b/c the def integral goes form 3 to 0

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1wanna go with  everything? i dont think it makes a diff :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1pi (3x^3 x^5/5 3x^4/2) then right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1pi * (((3) * ((3)^3))  (((3)^5) / 5)  ((3 * ((3)^4)) / 2)) = 25.4469005 is what google spits out ....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So do you think that's right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1i think so; you can double check it if you want.... but im pretty sure we worked the kinks out of it :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.1try to integrate one function at a time and subtract one from the other in the end to verify; kinda like making a donut and then cutting out the hole

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Nice way to check! Thanks again!
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