*CALC2 HELP PLEASE* The region enclosed by the curve x=sqrt(y), and by the lines x= -y and y=5 rotated around the x-axis.

- anonymous

- schrodinger

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- anonymous

Thanks for the medal, but do you have any tips?

- anonymous

well, what you've got yourself there is an integral with some pretty odd bounds, give me a second so I can draw a picture to see how to approach it.

- anonymous

Thanks man.. The shape is pretty funky..

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## More answers

- anonymous

is it 3d?

- anonymous

|dw:1327642062679:dw|

- anonymous

yeah it's rotating

- anonymous

another, question, which area contained by those lines?

- anonymous

It doesn't specify really, so I'm confused there as well..

- anonymous

The whole area I shaded in

- anonymous

Because graph is this

##### 1 Attachment

- anonymous

hmm.. that is really weird..

- anonymous

aww, I thought dumbcow had it figured out.. haha

- anonymous

so depending on what the area is its just a matter of doing the volume of revolution, but without knowing which specific area is... I want to assume that the area is the bit off to the left from y=-x up to y=5 and from y=-x over to y=x^2

- anonymous

did they specify x=+sqrt(y)?

- dumbcow

ok i think you can approach this using the washer method where you have an outer area - inner area
each cross section is a circle and you integrate wrt x from -5 to sqrt5
the outer radius would be 5 since that is the max y-value.
the inner radius would be the y-value of the appropriate function f(x)
|dw:1327642598764:dw|
\[\large V = \pi \int\limits_{-5}^{0}(25-x^{2}) dx + \pi \int\limits_{0}^{\sqrt{5}}(25-x^{4}) dx\]

- anonymous

dumbcow: after integration I got a negative volume?

- dumbcow

hmm no it should be positive
make sure when you evaluate you subtract upper limit - lower limit

- anonymous

ok let me try again

- anonymous

the integration would be.. pi(25x-x^3/3) and pi(25x-x^5/5), right?

- dumbcow

yes

- anonymous

http://www.wolframalpha.com/input/?i=%5Bpi+integral+%5B%5B25-x%5E2%5D%2C+%7Bx%2C-5%2C+0%7D%5D%5D+%2B+%5Bpi+integral+%5B%5B25-x%5E4%5D%2C+%7Bx%2C0%2C+sqrt%285%29%7D%5D%5D

- anonymous

I got 402.296 on wolfram, and it says incorrect on my homework.. :/

- anonymous

Nahhh I'm just kidding.. Worked perfect. Thanks guys!!

- dumbcow

isn't wolfram great.
ok well do they want in terms of pi?
i'll look at it again i may have made a mistake somewhere

- dumbcow

never mind :)

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