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 g
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 in
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,
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