Question

Find the volume of the region between the graph of f(x,y)=9−x^2−y^2 and the xyplane

Answer 1

hey

Answer 2

thank god

Answer 3

i got 2 questions left and i'm done with calc 3 forever

Answer 4

so xy plane is z=0

right?

Answer 5

yes

Answer 6

so we have to think about the region of integration

Answer 7

9−x^2

Answer 8

it's much easier when i can just pop it into wolfram lol

Answer 9

\[\int _{-3}^3\int _{-\sqrt{9-x^2}}^{\sqrt{9-x^2}}\left(9-x^2-y^2\right)dydx\]

Answer 10

holy crap you can actually do that?

Answer 11

pop it into wolfram lol

Answer 12

http://www.wolframalpha.com/input/?i=Plot3D%5B%7B9%20-%20x%5E2%20-%20y%5E2%2C%200%7D%2C%20%7Bx%2C%20-3%2C%203%7D%2C%20%7By%2C%20-3%2C%203%7D%5D&t=crmtb01

Answer 13

i gotta learn wolfram better

Answer 14

so you have a test today?

http://www.wolframalpha.com/input/?i=Integrate%5B9%20-%20x%5E2%20-%20y%5E2%2C%20%7Bx%2C%20-3%2C%203%7D%2C%20%20%20%20%20%7By%2C%20-Sqrt%5B9%20-%20x%5E2%5D%2C%20Sqrt%5B9%20-%20x%5E2%5D%7D%5D&t=crmtb01

Answer 15

no...just my last 2 homework questions

Answer 16

test was this past monday...just some lingering homework before the final

Answer 17

u got time for another if i make another post?

Answer 18

yep

Answer 19

awesome

Answer 20

I am sorry to see how many time you had to post this