Chapter 13: Q. 14 (page 1003)
Explain why using an iterated integral to evaluate a double integral is often easier than using the definition of the double integral to evaluate the integral.
Ans:
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Evaluate the iterated integral :
Evaluate each of the double integrals in Exercises 37โ54 as iterated integrals.
Explain how to construct a Riemann sum for a function of two variables over a rectangular region.
Describe the three-dimensional region expressed in each iterated integral in Exercises 35โ44.
In Exercises 57โ60, let R be the rectangular solid defined by
R = {(x, y, z) | 0 โค x โค 4, 0 โค y โค 3, 0 โค z โค 2}.
Assuming that the density at each point in R is proportional to the distance of the point from the xy-plane, find the moment of inertia about the x-axis and the radius of gyration about the x-axis.
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