Question

this should be easy.......

Find the volume of the solid enclosed by the paraboloids z=1(x^2+y^2) and z=18−1(x^2+y^2).

Answer 1

set the two equal and solve for r gets r=3. so i have...\[\int\limits_{0}^{2\pi}\int\limits_{0}^{3}18-2r^2 r dr dtheta\]giving an answer of 99pi/4. webwork says no. i just did this in the double integral section.....

Answer 2

hate to be a bother, but @ganeshie8, could you help me again?

Answer 3

that looks good to me, except for a missing parenthesis

Answer 4

\[\int\limits_{0}^{2\pi}\int\limits_{0}^{3}(18-2r^2) r dr dtheta\]

Answer 5

yeah, i put that into the wolfram alpha widget for polar....

http://www.wolframalpha.com/widgets/view.jsp?id=819a2d24e73f94fa5a05de2fad9ebddc

Answer 6

webwork says that answer is incorrect

Answer 7

well, i tried using that two ways. the firs time was 0 to 2pi, but it gave the same answer.

Answer 8

http://www.wolframalpha.com/input/?i=%5Cint%5Climits_%7B0%7D%5E%7B2%5Cpi%7D%5Cint%5Climits_%7B0%7D%5E%7B3%7D%2818r-2r%5E3%29+drd%5Ctheta

Answer 9

im getting 81pi ?

Answer 10

oh. i didn't know you had to put () around the equation in the first box or the widget would do it wrong.....grr. thanks.

Answer 11

yeah the widgest is simply attaching rdrdtheta at the end it seems

Answer 12

which is weird

Answer 13

it should multiply r by the entire integrand, not just the last term

Answer 14

i'll know that for next time. now i'm battling writing a triple integral six different ways.....

Answer 15

3! = 6

Answer 16

does your professor really hates u that much ?

Answer 17

lol. i guess. Express the integral ∭Ef(x,y,z)dV as an iterated integral in six different ways, where E is the solid bounded by z=0,x=0,z=y−x and y=2. i got the first four. struggling with dydzdx and dydxdz

Answer 18

should be 0 to 2, 0 to x, z+x to 2. but it doesn't like the 0 to x part.....can't figure out why.

Answer 19

for dydzdx :
x : 0->2
z : 0->-x
y : z+x->2


for dydxdz :
z : 0->2
x : 0->-z
y : z+x->2

Answer 20

see if they work

Answer 21

the -x and -z answers didn't work, @ganeshie8 . sorry for the delay, i just got home from work.

Answer 22

could u take a screenshot and attach again

Answer 23

yes, beccaboo. this is for the problem: Express the integral ∭Ef(x,y,z)dV as an iterated integral in six different ways, where E is the solid bounded by z=0,x=0,z=y−x and y=2.

Answer 24

try entering
-x+2

Answer 25

and
-z+2

Answer 26

respectively for the incorrect ones

Answer 27

ugh. finally! thank you, becca!

Answer 28

you're welcome :)