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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)
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