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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 12.3.2 .
Let
\(D\) be the region inside the unit circle centered at the origin, let
\(R\) be the right half of
\(D\text{,}\) and let
\(B\) be the bottom half of
\(D\text{.}\)
(a) On 3 separate plots, graph and label the regions
\(D\text{,}\) \(R\text{,}\) and
\(B\text{.}\)
(b)
For each double integral below, decide without calculation whether the double integral will be positive, negative, or zero. You should write a couple of sentences to explain your answer for each part.
\(\displaystyle \iint_D \; dA\)
\(\displaystyle \iint_D \; x \; dA\)
\(\displaystyle \iint_B \; x \; dA\)
\(\displaystyle \iint_R \; x \; dA\)
\(\displaystyle \iint_D \; x^2 \; dA\)
\(\displaystyle \iint_B \; -x^2 \; dA\)
\(\displaystyle \iint_R \; -e^x \; dA\)
\(\displaystyle \iint_B \; e^y \; dA\)
\(\displaystyle \iint_D \; xy \; dA\)
