Homework 9 - dθ dr(c Evaluate one o± your integrals to...

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APPM 2350 HOMEWORK 09 FALL 2010 Due Friday, October 29, 2010 at 4 pm under your TA’s door. 1. Consider the fnite triangular region in the frst quadrant bounded by x = 0, y = 0 and x + y = 1. (a) Using polar coordinates, set up the integral(s) to calculate the area o± the triangle in the order dr , . (b) Repeat the calculation above, but using double integrals in the order , dr . (c) Evaluate one o± your integrals to fnd the area. 2. Consider the fnite rectangular region in the frst quadrant bounded by x = 0, x = a , y = 0, and y = b ,where b>a . (a) Using polar coordinates, set up the integral(s) to calculate the area o± the rectangle in the order dr , . (b) Repeat the calculation above, but using double integrals in the order
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Unformatted text preview: dθ , dr . (c) Evaluate one o± your integrals to fnd the area. 3. Consider the fnite solid object bounded on the bottom by the sur±ace z = 0, on the top by x 2 + y 2 = z 2 , and the side by x 2 + y 2 = 1. (a) Using cartesian coordinates, set up the integral(s) to calculate the volume o± the object in the order dz , dy , dx . (b) Repeat the calculation above, but using the order dy , dz , dx . (c) Repeat the calculation above, but using the order dx , dy , dz . (d) Evaluate one o± your integrals to fnd the volume....
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This note was uploaded on 02/10/2011 for the course APPM 2350 taught by Professor Adamnorris during the Fall '07 term at Colorado.

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