Question

We have: \[\int_0^1 \int_{3y^2}^{4-y^2}\int_{-\sqrt{z-3y^2}}^{\sqrt{z-3y^2}} dxdzdy\]
Task: change the order of integral to dxdydz

Answer 1

\(
\large \int_0^1 \int_{3y^2}^{4-y^2}f(y,z)dzdy\)
does this simplify things ?
region between 2 parabolas...

Answer 2

I tried, but failed :(

Answer 3

plot z=y^2
z = 4-y^2
on same plane
taking y as vertical and z as horizontal

Answer 4

z=3y^2

Answer 5

Hold on! I think I catch my mistake, just a minute!

Answer 6

*staring at the screen*