Calculus II 
Test #1
March 5, 2002
R.  Hammack 
Score ______

(1) Evaluate the following integrals.
(a) [Graphics:Images/1S02Dsol_gr_1.gif]

(b) [Graphics:Images/1S02Dsol_gr_3.gif]

(c) [Graphics:Images/1S02Dsol_gr_9.gif]


(d) [Graphics:Images/1S02Dsol_gr_14.gif]

(2) A object moving on a straight line has a (nonconstant) acceleration of  6t  feet per second per second at time t. It travels a distance of 33 feet between times t = 0 and t = 3.  Find the object's velocity function v(t).


(3) [Graphics:Images/1S02Dsol_gr_54.gif]


(4) Find the average value of the function [Graphics:Images/1S02Dsol_gr_67.gif]on the interval [0, ln(2)].


(5) [Graphics:Images/1S02Dsol_gr_76.gif]

(6)  The graph of a function f(x) has slope [Graphics:Images/quiz1solved_gr_14.gif]  at each point (x, f(x)).
Also, the graph of  f(x) passes through the point (1, 5).  Find the function f(x).


(7)  The expression   [Graphics:Images/quiz2_gr_10.gif][Graphics:Images/quiz2_gr_11.gif]   represents a definite integral over the interval [3, 5].   Write the definite integral. (You do not need to find its value.)