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2. Express the area of the given surface as an iterated double integral in polar coordinates, and then find the surface area. (a) the portion of the cone z =√x2 + y2 that lies inside the cylinder x² + y² = 2x.

2. Express the area of the given surface as an iterated double integral in polar coordinates, and then find the surface area. (a) the portion of the cone z =√x2 + y2 that lies inside the cylinder x² + y² = 2x.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Express the area of the given surface as an iterated double integral in polar coordinates, and then find the surface area. (a) the portion of the cone z =√x² + y² that lies inside the cylinder x² + y² = 2x. (b) the portion of the paraboloid z=1-x² - y2 that is above the xy-plane. (c) the portion of the surface z = xy that is above the sector in the first quadrant bounded by the lines y = x/√3, y = 0, and the circle x² + y²=9. (d) the portion of the paraboloid 2z = x² + y² that is inside the cylinder x² + y² = 8. (e) the portion of the sphere x² + y² +2²=16 between the planes z = 1 and z = 2. (f) the portion of the sphere x². + y² + z² = 8 that is inside the cone z = √x² + y²₁
Transcribed Image Text:2. Express the area of the given surface as an iterated double integral in polar coordinates, and then find the surface area. (a) the portion of the cone z =√x² + y² that lies inside the cylinder x² + y² = 2x. (b) the portion of the paraboloid z=1-x² - y2 that is above the xy-plane. (c) the portion of the surface z = xy that is above the sector in the first quadrant bounded by the lines y = x/√3, y = 0, and the circle x² + y²=9. (d) the portion of the paraboloid 2z = x² + y² that is inside the cylinder x² + y² = 8. (e) the portion of the sphere x² + y² +2²=16 between the planes z = 1 and z = 2. (f) the portion of the sphere x². + y² + z² = 8 that is inside the cone z = √x² + y²₁
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