Chapter 13: Q. 24 (page 1027)
Each of the integrals or integral expressions in Exercises represents the area of a region in the plane. Use polar coordinates to sketch the region and evaluate the expressions.
Short Answer
The integral value is
Chapter 13: Q. 24 (page 1027)
Each of the integrals or integral expressions in Exercises represents the area of a region in the plane. Use polar coordinates to sketch the region and evaluate the expressions.
The integral value is
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Get started for freeLet be a lamina in the xy-plane. Suppose is composed of n non-overlapping laminæ role="math" localid="1650321722341" Show that if the masses of these laminæ are and the centers of masses are then the center of mass of is where
Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.
Find the masses of the solids described in Exercises 53–56.
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.
Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.
Let be a continuous function of three variables, let localid="1650352548375" be a set of points in the -plane, and let localid="1650354983053" be a set of points in -space. Find an iterated triple integral equal to the triple integral localid="1650353288865" . How would your answer change iflocalid="1650352747263" ?
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