?Evaluate the iterated integrals.Let D be the region bounded by \(y=1-x^2,\ y=4-x^2\)
Chapter 5, Problem 86(choose chapter or problem)
Evaluate the iterated integrals.
Let D be the region bounded by \(y=1-x^2,\ y=4-x^2\) and the x - and y - axes.
a. Show that \(\iint_{D} x d A=\int_{0}^{1} \int_{1-x^{2}}^{4-x^{2}} x d y d x+\int_{1}^{2} \int_{0}^{4-x^{2}} x d y d x\) by dividing the region D into to regions of Type I.
b. Evaluate the integral \(\iint_{D} x d A\).
Text Transcription:
D
(y=1-x^2,\ y=4-x^2
x - and y - axes
\iint_{D} x d A=\int_{0}^{1} \int_{1-x^{2}}^{4-x^{2}} x d y d x+\int_{1}^{2} \int_{0}^{4-x^{2}} x d y d x
\iint_{D} x d A
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