265Lesson15Problems - Use an iterated integral to compute...

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MATH 265: MULTIVARIABLE CALCULUS: LESSON 15 PROBLEMS Problems are worth 20 points each. Warning: It will be very difficult to get the correct limits of integration without a sketch of the curves that bound the region over which the integral is taken. (1) Evaluate Z 1 0 Z y y 2 xe y d x d y . (2) Integrate f ( x,y ) = xy over the region R between the parabola y = x 2 and the line y = 2 x + 3. (3) Evaluate ZZ T ( x - y ) d A where T is the region between the graphs of y = sin x and y = cos x for 0 x π 4 . (4) Evaluate ZZ D sin x x d A where D is the region in the first quadrant bounded by the lines x = 1, x = 2, y = x , and y = 2 x . (5) Reverse the order of integration and evaluate Z 1 0 Z 1 y e - x 2 d x d y . (6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.)
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Unformatted text preview: Use an iterated integral to compute the area of the ellipse x 2 a 2 + y 2 b 2 = 1. The a and b are positive constants. (Hint: You will need to use a trigonometric substitution to do one of the integrations. You may need to review that method in the text. There are going to be quite a few complicated integrals for the rest of the course, so you’ll probably get many opportunities to review integration techniques covered in Calculus II. Might as well put a bookmark in that section of the text right now.) 1...
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This note was uploaded on 02/24/2011 for the course MATH 265 taught by Professor Jerrymetzger during the Winter '11 term at North Dakota.

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