taking slices at fixed y, how do i find the vol of the solid enclosed by y=x^2, y+z=2 and z=1?
You need a "floor" for your solid - I'm going to assume z=0.
You divide the solid into two parts - the first part, with y going from 0 to 1, has the z=1 plane on the top. The second part, with y going from 1 to 2, has the y+z=2 plane on the top. All of the cross sections are rectangles.
where I substituted length times width for the area in both cases. Of course, the total volume is .
Post again in this thread if you're still having trouble.
may i know how ((2-y)-0) for V2 is obtained? i thought that the lenght for y would be (2-1)?
Also, how do you know that we can use a single integral to find the vol? i thought that double integrals are mean for areas and triple integrals are meant for vol?
When I substituted length times width for the cross-sectional area, I actually did an (extremely easy) double integral. So that makes three integrals for a volume.