MAC 2312 Lecture 9: 7.8 improper integrals
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20 Jun 2018
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Monday
June 4th
Improper Integrals
Type I
°
. Infinite Integral
(a) If
fta f(x)dx
ex
.
,g+s
,
for all t2 a then
fda fcx )=II -ftafcx )
*if not exist then
f]fcx )is divergent
(b) ±ff[ fcx )exists for an + £a
(c) f9¥2 d×
then (d) f?Idx
[a
fcx )d×III .foffcx )
(convergent is limit exists )
(divergent if not )
*
).[ fcx )dx =
ftp.cx)+f[fct )
0
Example 1f×e× dx
-a
Soln :
f{ Xexdx = ×e×|I -fg ex d×
fC×)=× gicx )=e×
= xe× -e×1E =.i-[tet -et ]^
lim o
t-> of xexdx =
lin (-I+ et -tet )
f6- -7 a÷<
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