**Calc2 Help Needed**
Find the volume of the solid generated by revolving the described region about the given axis:
The region bounded above by the line y=6 , below by the curve y=sqrt(x), and to the left by the y-axis, rotated along the following lines:
x=36

- anonymous

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- dumbcow

another one huh :)

- anonymous

Yep.. I'm going to start tutoring next week. I am having the worst time with these..

- dumbcow

try drawing out the region to get the bounds

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## More answers

- anonymous

yep, i've got that

- anonymous

|dw:1327644073706:dw|

- anonymous

so the bounds should be in y? so 0 to 6

- anonymous

I was thinking of using the cylindrical shell method

- anonymous

2pi integral (radius)height

- anonymous

radius = y height = y-36?

- dumbcow

i'm not as familiar with the shell method, mostly because i don't like using it
anyway, wouldn't the radius be in terms of x, and the height be 6-y

- anonymous

oh yes..

- anonymous

so we would use the disc method?

- anonymous

so radius = y^2 and height is 6-y?

- dumbcow

you could use either i believe for this one.
if you used the disc method:
outer radius = 36
inner radius = 36-y^2
...yes

- anonymous

so we have the integral of pi(36-36+y^2)?

- dumbcow

think area of circle: A = pi*r^2

- anonymous

forgot the ^2

- dumbcow

what should you integrate from, or what are the bounds

- anonymous

0 to 36?

- dumbcow

the outer radius is 36 right, that is in x-direction
now imagine the figure being sliced horizontally so we integrate over y
what are the bounds of y

- anonymous

oh 0 to 6 in terms of y

- dumbcow

yep

- anonymous

ok so from 0 to 6 integral (36 - 36 + x^2)^2?

- anonymous

= pi(y^5/5)

- dumbcow

not quite
its R^2 - r^2 Not (R-r)^2
-> 36^2 - (36-y^2)^2

- dumbcow

because you're not subtracting the radius, you are subtracting the areas

- anonymous

ohh.. do I have two separate integrals?

- dumbcow

no just keep them separate...you can simplify it

- anonymous

nvm.. i see now

- anonymous

I got it right!! yay.. haha.. =3628.8pi. Thank you so much!

- dumbcow

great...welcome

- anonymous

Now it's time to study biology... fun :/

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