Question

again this answer is incorrect i set the limits as -10 13 years ago

Answer 1

i assume itll look something like this than

Answer 2

x=a..b
y=0..f(x)
z=-10..f(x,y)

Answer 3

umm whats f(x) in this case?

Answer 4

hmmm, y=x+4 in the xy plane

Answer 5

and since the plane is horizontal to begin with; it transfers down to the z=-10 plane

Answer 6

where does the y=o and y=x+4 planes intersect the 3rd plane?

Answer 7

not quite shire

Answer 8

urg!! my touchpad on the laptop is too sensitive, and goes flying off to wherever the cursor is hovering if i get to close to it :/

Answer 9

x=-4..7
y=0..(x+4)
z=4-2x-y

Answer 10

\[\int_{-4}^7\int_{0}^{x+4}4-2x-y~dy~dx\]

Answer 11

i forgot the -10 :) which is just a +10 on the function part

Answer 12

\[\int_{-4}^7\int_{0}^{x+4}4-2x-y+10~dy~dx\]
\[\int_{-4}^714(x+4)-2x(x+4)-\frac12(x+4)^2~dx\]

Answer 13

im really confused on how came to this conclusion isnt this the graph on the x y axis??

Answer 14

in the xy plane yes, but the base of it all is still 10 below that

Answer 15

i get the z limits but the limits for y and x have me confused could you explain em plx

Answer 16

for the x, i just lowered it down to the base plane; y=0 and z=-10

2x+y+z = 4
2x+0-10=4
2x = 14; x=7

and of course it still has the y=x+4 limit in the z=-10 plane; y=0=x+4; x=-4

Answer 17

but i think i see that if i keep it as such, i might need a split in the y

Answer 18

2x+x+4 - 10 = 4

3x = 10

x=3' 1/3 seems to split there in the z=-10 plane; might have to think of doing the limits in another fashion eh

Answer 19

hey there are many ways to do this i got the answer using my way incase you are curious=)

Answer 20

as long as its the right answer, id like something to compare with yes :)

Answer 21

ok, so my idea is, the y values change from 10/3 to 7 giving us a separate integration:

\[\int_{-4}^{10/3}\int_{0}^{x+4}\int_{-10}^{4-2x-y}dzdydx+\int_{-4}^{10/3}\int_{0}^{-2x+14}\int_{-10}^{4-2x-y}dzdydx\]

\[\int_{-4}^{10/3}\int_{0}^{x+4}14-2x-y~dydx+\int_{-4}^{10/3}\int_{0}^{-2x+14}14-2x-y~dydx\]


\[\int_{-4}^{10/3}4x+54-2.5x^2~dx+\int_{-4}^{10/3} -42x+98+3x^2~dx\]

and as slow as this computer is, i got no idea if thats right yet ..... better done on paper i spose

Answer 22

yep, 295.777777