Chapter 7 / Test 7 Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The function v(t) is the velocity in m/sec of a particle moving along the x- axis. Find the total distance traveled by the particle. 1) v(t) =t2 - 5t +4, 0 t 4 1) A) 13 B) - 8 C) 19 D) 103 2 3 3 6 Solve the problem. 2) A particle moves along the x- axis (units in cm). Its initial position at t =0 sec is x(0) =11. The figure shows the graph of the particle's velocity v(t). The numbers are the areas of the enclosed regions. 2) 16 a b c 11 69 What is the total distance traveled by the particle between t =0 and t =c? A) - 64 cm B) 96 cm C) - 42 cm D) 107 cm 3) A bathroom scale is compressed 1 in. when a 180 lb person stands on it. Assuming that the 3 scale behaves like a spring that obeys Hooke's law, how much does someone who compresses the scale 1 in. weigh? 6 A) 135 lb B) 45 lb C) 90 lb 1 D) 360 lb 3) Find the area of the shaded region. 4) f(x) =x3 +x2 - 6x, g(x) =6x 4) y 25 20 15 10 5 5 4 3 2 1 5 10 15 20 (4, 24) 25 A) 768 12 (3, 18) (0, 0) 1 2 3 4 5 x C) 937 12 B) 81 12 D) 343 12 Find the area enclosed by the given curves. 5) Find the area of the propeller- shaped region enclosed by the curve x - y 3 =0 and the line x - 4y =0. A) 8 B) 31 C) 4 D) 17 2 4 Find the area of the regions enclosed by the lines and curves. 6) x - 1 =2y 2, x =y +4 A) 3 B) 9 C) 125 2 24 5) 6) D) 149 24 Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x- axis. 7) y =6cos (x), y =6, x = -0.5, x =0.5 7) A) 36 B) 72 C) 12 D) 18 Find the volume of the solid generated by revolving the region about the given line. 8) The region in the first quadrant bounded above by the line 3x +y =6, below by the x- axis, and on the left by the y- axis, about the line x = -2 A) 32 B) 64 C) 5 D) 24 8) Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x- axis. 9) x =8y - y 2, x =0 9) A) 256 B) 2048 C) 1024 D) 4096 3 3 3 3 2 Find the exact length of the curve analytically by antidifferentiation. x 10) y = t2 - 1 dt , 4 x 7 10) 1 A) 33 2 B) 22 C) 12 D) 33 Find the work done by the force of F(x) newtons along the x- axis from x =a meters to x =b meters. 11) F(x) =xe - x/5, a =0, b =6 A) 6.928 J B) 15.964 J C) 14.458 J D) 8.434 J Solve the problem. 12) A force of 4 N will stretch a rubber band 5 cm. Assuming Hooke's law applies, how much work is done on the rubber band by a 12 N force? A) 0.3 J B) 0.9 J C) 0.1 J D) 9000 J 3 11) 12)