?Evaluate the iterated integrals.Let D be the region bounded by \(y=x^2,\ y=x+2\), and
Chapter 5, Problem 89(choose chapter or problem)
Evaluate the iterated integrals.
Let D be the region bounded by \(y=x^2,\ y=x+2\), and \(y=-x\).
a. Show that \(\iint_{D} x d A=\int_{0}^{1} \int_{-y}^{\sqrt{y}} x d x d y+\int_{1}^{2} \int_{y-2}^{\sqrt{y}} x d x d y\) by dividing the region D into two regions of Type II, where \(D=\left\{(x, y) \mid y \geq x^{2}, y \geq-x, y \leq x+2\right\}\).
b. Evaluate the integral \(\iint_{D} x d A\).
Text Transcription:
D
y=x^2
y=x+2
y=-x
\iint_{D} x d A=\int_{0}^{1} \int_{-y}^{\sqrt{y}} x d x d y+\int_{1}^{2} \int_{y-2}^{\sqrt{y}} x d x d y
D=\left\{(x, y) \mid y \geq x^{2}, y \geq-x, y \leq x+2\right\}
\iint_{D} x d A
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