Calculus II 
Quiz #2 
February 22, 2002
R.  Hammack 
Score ______

(1)   Find the following definite integrals by analyzing the graph of the integrand. Be sure to include a sketch of the graph and indicate how it gives your answer.

(a)  [Graphics:Images/quiz2_gr_1.gif][Graphics:Images/quiz2_gr_2.gif]13/2

(Because the region under the graph consists of two triangles, one with base and height 2, and the other with base and height 3.)


(b)   [Graphics:Images/quiz2_gr_4.gif][Graphics:Images/quiz2_gr_5.gif]= [Graphics:Images/quiz2_gr_6.gif]

(One half the area of a circle of radius 3.)


(c)  [Graphics:Images/quiz2_gr_8.gif] 0  

 (Because area below x-axis cancels area above x-axis.)


(2)  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.)    ANSWER:[Graphics:Images/quiz2_gr_12.gif]

(3) Suppose  f  is a function for which [Graphics:Images/quiz2_gr_13.gif]= 5   and [Graphics:Images/quiz2_gr_14.gif]= 9.   
One of the definite integral properties says [Graphics:Images/quiz2_gr_15.gif] , and this gives  [Graphics:Images/quiz2_gr_16.gif]Therefore:
(a) [Graphics:Images/quiz2_gr_17.gif]5-9 = -4
(b)  [Graphics:Images/quiz2_gr_18.gif](-4)(-4) = 16

(4) Find [Graphics:Images/quiz2_gr_19.gif]    if  [Graphics:Images/quiz2_gr_20.gif]   and   [Graphics:Images/quiz2_gr_21.gif]
[Graphics:Images/quiz2_gr_22.gif] = 5+2(-3) = -1