# Thread: multiple integrals reversing order of integration

1. ## multiple integrals reversing order of integration

can you solve for me please

0 to 4(for the 1st integral) y^.5 to 2 (for the 2nd) (x^3 + 1)^0.5 dxdy?

2. $\int_0^4 {\int_{\sqrt y }^2 {\sqrt {x^3 + 1} \,dx} \,dy} .$

Two ways to reverse integration order:

1. Make a sketch to see where the integral is taken.
2. Playin' with inequalities.

3. hello thanks for your reply. I think for the reverse it would be 0 to 2, x^2 to 4 fcn dydx but i do not know how to integrate that fcn. i think that that fcn cannot be integrated with respect to x and that's why you reverse the order. however, i may have done something incorrectly and can't see it, but i'm getting to have to integrate it anyways, but it's counterpart i could deal with via substitution.

4. It's actually $\int_0^2 {\int_0^{x^2 } {\sqrt {x^3 + 1} \,dy} \,dx} .$

So $\int_0^2 {x^2 \sqrt {x^3 + 1} \,dx} ,$ and this is very easy, just set $z^2=x^3+1.$

5. thanks so much!