MAC 2312 Midterm: MAC2312 F14 Test 1
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Instructions: write your complete solutions on your answer sheets. No graphing calculators are allowed to be used. To receive credit, you must show all work. You are not required to simplify your answers. Some answers will involve fractions, logarithms, etc (1) (40 pts. ) Do not evaluate the integral. (c) set up an integral for the volume of the solid generated when r is revolved about the y-axis. Do not evaluate the integral. (d) find x, the x-coordinate of the centroid of r. (2) (30 pts. ) Let c denote the curve de ned by y = 1+cos 3x, where 0 x 2 /3. In this case, do not evaluate the integrals. (a) the length of c, (b) the area of the surface generated when c is revolved about the (i) x-axis (ii) y-axis. 0 x 7. (3) (10 pts. ) Find the average value of the function f (x) = 7 x on the interval (4) (20 pts. )
