Chapter 13: Problem 16
Find the distance between the two points. $$ (8,-2,2),(8,-2,4) $$
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Evaluate the double integral. $$ \int_{0}^{4} \int_{0}^{x} \frac{2}{x^{2}+1} d y d x $$
Evaluate the partial integral. $$ \int_{0}^{\sqrt{4-x^{2}}} x^{2} y d y $$
Evaluate the double integral. $$ \int_{0}^{1} \int_{0}^{y}(x+y) d x d y $$
Use a symbolic integration utility to evaluate the double integral. $$ \int_{0}^{2} \int_{\sqrt{4-x^{2}}}^{4-x^{2} / 4} \frac{x y}{x^{2}+y^{2}+1} d y d x $$
The population density (in people per square mile) for a coastal town can be modeled by \(f(x, y)=\frac{120,000}{(2+x+y)^{3}}\) where \(x\) and \(y\) are measured in miles. What is the population inside the rectangular area defined by the vertices \((0,0)\), \((2,0),(0,2)\), and \((2,2) ?\)
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