Question

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

Answer 1

since we are only interested in changing the order of x and z, we may totally ignore dy, and the 3rd integral 0 to 1, and treat the 'y' as constant.
so, basically you're dealing with,
\(\large \int \limits_{-b}^{b} \quad \int \limits_{x^2+a}^{c}dzdx\)
does that simlify things ?

Answer 2

Hmm, it still looks complicated :(

Answer 3

ofcourse, after we are done, we will resubstitute for y

Answer 4

z=x^2+a is parabola
z=c
x=-b
x=b
are 3 lines

Answer 5

in x-z plane