Chapter 13: Q 13. (page 1066)
What are the six forms used to express the volume increment when you use rectangular coordinates to evaluate a triple integral? How do you decide which order to use?
Short Answer
The six forms are , , , , .
Chapter 13: Q 13. (page 1066)
What are the six forms used to express the volume increment when you use rectangular coordinates to evaluate a triple integral? How do you decide which order to use?
The six forms are , , , , .
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Get started for freeIn 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.
Find the masses of the solids described in Exercises 53โ56.
The first-octant solid bounded by the coordinate planes and the plane 3x + 4y + 6z = 12 if the density at each point is proportional to the distance of the point from the xz-plane.
State Fubini's theorem.
Explain why it would be difficult to evaluate the double integrals in Exercises 18 and 19 as iterated integrals.
Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32
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