Recent content by mistahkurtz

Well, I think I've progressed a bit towards finding an answer. I think I know how to redefine D_1. This D_1 = \{x \in R^3 \mid 0 \leq x_1 \leq 1, 0 \leq x_3 \leq \sqrt{5 - x_1}, 0 \leq x_2 \leq 5 -x_1 - x_3^2\} is wrong because the upper limit of x_2 should be the minimum of 1 - x_1 and 5...

I thought about doing that. But wouldn't the integral no longer be "an integral of a function f(x) over the region D," as the problem explicitly states, but rather "an integral of a function f(\Phi(x)) over the region \phi(D)" where \Phi(x) is the linear transformation that rotates the...

Homework Statement 2. The attempt at a solution It's not hard to find two orders of integration. (1) Integrate first with respect to x_3, then with respect to x_2, and then with respect to x_1, by dividing D into two regions: D = \{x \in R^3 \mid -1 \leq x_1 < 0, -\sqrt{1-x_1^2}...

Homework Statement Just a clarification: the two last equations must hold in an open neighborhood of the point (2, 1, -1, -2), not just at that point. Homework Equations The Attempt at a Solution I have to do an existence proof. The shortest way of accomplishing this would...