Problem 22. [1 point] Find the volume of the solid obtained by rotating the region enclosed by the curves y = 25x2, y = 20v2 and x = 0 about the y-axis. A) 187 B) 147 C) 137 D) 127 E) 167 Problem 23. [1 point] Find the volume of the solid obtained by rotating the region bounded by y = Inc, y = 0 and r = 5 about the line r = 5. A) [ 7(5-Inx)2 dr B) Jon5 7(5-ev)? dy C) f5 7(5-ev)? dy D) fix (25-(Inx)?) dr E) fans T (25 - e2y) dy Problem 24. [1 point] A rectangular swimming pool 6 m long, 5 m wide, and 4 m deep is full of water. Find the work needed to pump all of the water out of the swimming pool. (Use the facts that the density of water is 1000 kg/m3 and g = 9.8 m/s2.) A) 2360640 J B) 2357760 J C) 2340480 J D) 2352000 J E) 2346240 J Problem 25. [1 point] Suppose that the temperature of a cup of coffee t minutes after it is poured is given by T(t) = 22 + 72e-kt, where k = 51 Find the average temperature of the coffee during the first 22 minutes after it is poured. A) 4156 - 3672e-61 B) 2078 11 11 1836 e-51 C) 22 - 1836 e-51 D) 2078 - 1836e-51 E) 556 22 Problem 26. [1 point] Let f be a twice differentiable function with f ( 4 ) = 7 , [f ( 20 ) dx - 5 , [ f' ( x ) dx = 2 , and Use integration by parts to evaluate foxf'(x) dx. A) 23 B) 27 C) 19 D) 15 E) 11 Problem 27. [1 point] Evaluate the following integral: A) 64 + 382e B) 64 + 380e7 C) 64 + 381e? D) 64 + 384e ? E) 64 + 385e7 Problem 28. [1 point] A function f(r) is differentiable for all r and the equation f(x) = 0 has 7 distinct real roots. According to the Mean Value Theorem, what is the minimum number of critical numbers of f(x) ? A) 1 B) 3 C) 4 D) 6 E) 7