Find the volume in the first octant bounded by the coordinate planes, y=4, the plane (x/3) +(z/5) =1.

Question

anonymous · Answer

Double integral problem

anonymous · Answer

Y end points is 0 to 4,
I can solve for z to find the top
what about x?

dumbcow · Answer

My guess would be since we are talking about the first octant that all values have to be positive, x goes from 0 to 3
-> z = 5-(5/3)x
z bounded from 0 to 5
->x = 3 - (3/5)z
x bounded from 0 to 3

anonymous · Answer

How did you determine x?

dumbcow · Answer

i might be oversimplifying this but it seems that this forms a right triangular prism where actually you could do it without integrals
V = (1/2)*5*3*4 = 30

If im mistaken i apologize

anonymous · Answer

I understand. It is an exercise: they are trying to teach us how to set up double integrals.

dumbcow · Answer

oh ok
To determine x look at the linear relationship between z and x, x has to be between 0 and 3 for z to be positive

anonymous · Answer

thanks, i'll take a closer look