MHB Double & Triple Integrals: Same Solution?

[ineedhelpnow]

when taking double or triple integrals, do you get the same solution no matter which variable you integrate with respect to first?

 

[Prove It]

when taking double or triple integrals, do you get the same solution no matter which variable you integrate with respect to first?

You have asked a fat question there. You will get the same solution no matter what order you choose to integrate the variables in as long as you have set up the integral boundaries in each case, and as long as it is possible to find an antiderivative of the integrand in each way (sometimes you can't, which is why it is important to know how to reverse the order of integration).

 

[ineedhelpnow]

what do you mean by how to reverse the order of the integrand? say if you have like $\int_{0}^{2} \, \int_{0}^{4} \, \int_{1}^{2} \ NHN, dy dx dz$ , that would be the same as $\int_{0}^{4} \, \int_{0}^{2} \, \int_{1}^{2} \ NHN, dx dy dz$, right?a fat question? (Wondering)