Question

Integrals

Answer 1

\[\int\limits_{}^{}\int\limits_{}^{}\int\limits_{}^{}2z dx dy dz\]
\[0\le z \le1\]
\[2\le x \le 2y\]

Answer 2

\[\int\limits_{0}^{1}\int\limits_{0}^{x}\int\limits_{2}^{2y}2z dxdydx\]

Did i set this up right?

Answer 3

Im confused because when I work it out I am not getting a real number, but a function in terms of x. Do I need to do a change of variable?

Answer 4

MY overal answer was (x(x-2))

Answer 5

why do you put 0 to x for your interval of y?

Answer 6

oh sorry i forgot the bounds of y are given I just didnt write it here.

0<y<x

Answer 7

I see, so you introduced x again when you integrate over y, but you've just integrated over x, so you made x diappear by integrating over it, but the x term on the y interval made it reappear

Answer 8

Right

Answer 9

I am kind of confused about how to do it properly, its being awhile since I did my Calc III

Answer 10

Yea, its got myself and the 6 people im studying with stumped

Answer 11

let me get on wolfram alpha and see if it gives a solution

Answer 12

thanks!

Answer 13

wolframalpha says your right

Answer 14

it is a function of x after all, I guess this function of x is the correct answer, you didnt make a mistake anywhere

Answer 15

wait are second, what's your d's? dxdydx or dxdydz?

Answer 16

because these two gives different answes

Answer 17

Word of advice, don't always trust WA's results for multiple integrals. They still have a few kinks to work out.

Answer 18

if you have dxdydx, as your second post, then it has a definite value. But your first one says dxdydz which is x(x-2) and we cant do anything about it

Answer 19

its 2z dxdydx

Answer 20

hold on, that still doesnt make sense

Answer 21

becuase now you cant even get rid of your z, because you are not even integrating over it

Answer 22

God, sorry im such a clutz right now. I typed it wrong again. Ive been doing integrals for the past 32 hours.

its 2z * dx dy dz

Answer 23

then I think its correct to say its x(x-2), but I forgot mot of my multicalc stuff from my freshman year

Answer 24

Alrighty, thank you!