9 - Jignesh Patel due 11/28/2010 at 11:59pm EST. Assignment...

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Unformatted text preview: Jignesh Patel due 11/28/2010 at 11:59pm EST. Assignment 9 MATH262, Fall 2010 1. (1 pt) ZZ Using polar coordinates, evaluate the integral y2 )dA where R is the region 9 ≤ x2 + y2 ≤ 81. R sin(x2 + A cylindrical drill with radius 1 is used to bore a hole throught the center of a sphere of radius 2. Find the volume of the ring shaped solid that remains. 5. (1 pt) Z ZA. Using polar coordinates, evaluate the improper integral R2 ? 2. (1 pt) Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x2 + y2 = 36 and x2 − 6x + y2 = 0. e−5(x 2 +y2 ) dx dy. Z∞ B. Use part A to evaluate the improper integral −∞ e−5x dx. 2 6. (1 pt) Find the volume of the solid enclosed by the paraboloids z = 16 x2 + y2 and z = 2 − 16 x2 + y2 . 3. (1 pt) Use the polar coordinates to find the volume of a sphere of radius 10. 7. (1 Z Z Use cylindrical coordinates to evaluate the triple inZ pt) tegral x2 + y2 dV , where E is the solid bounded by the circular paraboloid z = 16 − 1 x2 + y2 and the xy -plane. 4. (1 pt) Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester E 1 ...
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This note was uploaded on 12/21/2010 for the course MATH 262 taught by Professor Faber during the Fall '08 term at McGill.

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