Activity 12.4.2

Let $D$ be the region inside the unit circle centered at the origin, let $R$ be the right half of $D$, and let $B$ be the bottom half of $D$.

1. On three separate plots, graph and label the regions $D$, $R$, and $B$.

2. For each double integral below, decide without calculation whether the double integral is positive, negative, or zero. Write a sentence or two to explain your answer for each part.

   1. $\iint_D \; 1\; dA$
   2. $\iint_D \; x \; dA$
   3. $\iint_B \; x \; dA$
   4. $\iint_R \; x \; dA$
   5. $\iint_D \; x^2 \; dA$
   6. $\iint_B \; 2-x^2 \; dA$
   7. $\iint_R \; -e^x \; dA$
   8. $\iint_B \; 1-e^y \; dA$
   9. $\iint_D \; xy \; dA$