Chapter 13: Q. 24 (page 1082)
Using polar coordinates to evaluate iterated integrals: Evaluate the given iterated integrals by converting them to polar coordinates. Include a sketch of the region.
Chapter 13: Q. 24 (page 1082)
Using polar coordinates to evaluate iterated integrals: Evaluate the given iterated integrals by converting them to polar coordinates. Include a sketch of the region.
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Get started for freeLet be a continuous function of three variables, let be a set of points in the -plane, and let be a set of points in 3-space. Find an iterated triple integral equal to the the triple integral. How would your answer change if?
Use Definition to evaluate the double integrals in Exercises .
where
Let f(x, y, z) and g(x, y, z) be integrable functions on the rectangular solid . . Use the definition of the triple integral to prove that :
Find the masses of the solids described in Exercises 53–56.
The solid bounded above by the hyperboloid with equation and bounded below by the square with vertices (2, 2, −4), (2, −2, −4), (−2, −2, −4), and (−2, 2, −4) if the density at each point is proportional to the distance of the point from the plane with equationz = −4.
In Exercises 45–52, rewrite the indicated integral with the specified order of integration.
Exercise 42 with the order dy dx dz.
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