Decide, without calculation, if each of the integrals below are positive, negative, or zero. let d be the region inside the unit circle centered at the origin. let t, b, r, and l denote the regions enclosed by the top half, the bottom half, the right half, and the left half of unit circle, respectively.1. ∬b xe^xda2. ∬r xe^xda3. ∬t xe^xda4. ∬d xe^xda5. ∬l xe^xda? positive negative zero

The integrals over B and T will be positive. Keeping fixed, is strictly increasing over D as increases, so the integrals over (i.e. the bottom/top left quadrants of D) is negative but the integrals over are *more* positive.

The integrals over R and L are zero. If we take , then , which is to say is symmetric across the -axis. For the same reason, the integral over all of D is also zero.