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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 12.4.3 .
Suppose we want to find the area of the bounded region \(D\) between the curves
\begin{equation*}
y = 1-x^2 \quad \quad \text{ and } \quad \quad y=x-1
\end{equation*}
Figure 12.4.2. The graphs of \(y = 1-x^2\) and \(y=x-1\)
(a) The volume of a solid with constant height is given by the area of the base times the height. Hence, we may interpret the area of the region
\(D\) as the volume of a solid with base
\(D\) and of uniform height 1. That is, the area of
\(D\) is given by
\(\iint_D 1 \, dA\text{.}\) Write an iterated integral whose value is
\(\iint_D 1 \, dA\text{.}\)
Hint .
Which order of integration might be more efficient? Why?
(b) Evaluate the iterated integral from (a). What does the result tell you?
