\ff. S(3x4 + 5x-3 - 2) dx = g. S(2x2 - 2)2 dx = h . SV1 + Jy dy = cos 2x . 3 sin x cos x dx =\f3 3. What is the average value of g(x) = x 2 VX + 1 on the interval [0, 2]? 1;2 If the substitution \\f = sin y is made in the integrand of f0 V1 ' X dx, the resulting integral is . (4 points possible) J11 The area under the curve y = cos x from x = a to x = 2 is 0.2. What is the value of a rounded to three decimal places? (4 points possible) 3n 6. For 0 5 ts 2 , a particle moves along the x-axis. The velocity of the function is given by v(t) = sin(2t). The particle is at the position x = 2 when time is t= 0. (18 points possible) 3:: a. Find the total distance traveled by the particle on the time interval 0 5 is 2 . 3a: b. Find the particle's displacement on the time interval 0 5 ts 2 . c. What is the acceleration of the particle at time t= 3? Is the particle speeding up or slowing down? Explain. d. Find the position of the particle at time 1': 3. 7. Find the derivatives of the following functions and identify and justify the rule or theorem you use to find each. (25 points possible) 2(t- 1) a. g(t) = 2 b. y = In(tan x) C. j(x) = Vcos(5x) + etan x d. y= Vt + esint 1 + W e. f(w) = In (1 - w8. If f and g are continuous functions, a fa 9(x) dx, determine if each statement below is true or false. If the statement is true, explain how you know. If the statement is false, provide a counterexample with an explanation. a. Salf(x) - 9(*)x > 0. b. f( x) > g(x). c . Salf(x ) lax > Sal9( x) lax. Justify your answers. (9 points possible) e 2 x 0