Homework for Chapter 6.1: Area between Curves For the problems that involve a little bit of numeric computation, feel free to use Excel or some other similar program. Drill problems: 9 y=1/x, y=1/x^2, x=2 14 y=cos x, y=2-cos x, x between 0 and 2pi 20 4x+y^2 = 12, x=y 22 y=sin(pi x/2), y=x 30 area of the triangle (0,5) (2,-2) (5,1) 34 y=cube root of (16-x^3), y=x, x=0; use the Midpoint rule with n=4. Applied problems: 42 area of a pool: assume that each end of the pool has a measurement of 0 meters wide. Use the midpoint rule with n=4 (not n=8) 44 birth and death rates Question A: Some solar power systems use a parabolic mirror to focus sunlight on a tube that absorbs heat. An example picture is at http://en.wikipedia.org/wiki/Parabolic_trough Suppose that you point the mirror straight up and look at a cross-section from the side, so you see a thick parabola. The front (upper) surface of the mirror is defined by the function f(x) = 0.25 x^2 + 0.01 and the back (lower) surface is defined by
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Archimedes, Parabolic reflector, solar power systems, Midpoint Rule, maximum departure rate