Exerclse Find
3
/
ALrea and the Fundamental Theore1Fl of Ca1culus
Let/be a nolln
1the and c() inuo RIn on on ed ed i x/al lc .The
1
,the axis,and the lirxB =: aIld
J=b is denoted =1bounded by the graph of j
by
(
lb
)d
The expression s`/( )dt is called
Using the Log Ru1e:
Rec lthe P( 'er
R1 h:
Note that t11e Powcr Rule not v for Q=1 To i egrate functions such as
^
1d W use the Log Rulcs
r:dt=ln u+c
dt=Jf d. ln u+c
r
Example Find the fo11owing integr 1
1
2
V
j
dq
t
d
l
f
t`'cfw_ d
= h  C,
`
^ld
2
Exponential and Logarithn1ic Integrals
Rules for Integr s of Exponential Funcuons:
re d
=eJ+C
=/e. =e.+C
/e :
Example Find the following integr
1,r4eJ
s
:l+d C,
,
k=J hd% c

O
bX
2,
C,
3.re 5dJ,
=qu
5
#:
=
C
r h
4
F3 e
2d
tA
,
^x
^
:2x
xc^
Jb=
NAME
I.D.#
Instructions: This exam consists of 8 multiple choice questions and 6 long
answer questions on 12 pages.
Place your answers to the multiple choice questions in the boxes below. You
may use the backs of pages for short and long answer questions.