2Blecture6 - LAST
DAY
 TO
DROP


Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: LAST
DAY
 TO
DROP
 =


Friday,
October
8th,
at
5PM
 LAST
DAY
 TO
ADD
 =


Friday,
October
15th,
at
5PM
 WAITLIST
 DEACTIVATED
 =


Friday,
October
8th,
at
5PM




 At
this
'me
waitlisted
students
will
no
longer
be
automa'cally
moved
from
the
 waitlist
to
the
course
should
spaces
become
available.

 The
only
way
to
add
to
the
course
is
through
StudentAccess/WebReg.

 The
SubsCtuCon
Rule
 Sec&on
5.5
 The
subs&tu&on
rule
is
used
to
solve
integrals
of
the
form
 

































f(g(x))
g’(x)
dx
 where
g
is
a
differen&able

func&on,
and
f
is
a
func&on
which
is
 con&nuous
on
the
range
of
g.
 It
states
that
the
integral
 


































f(g(x))
g’(x)
dx
 If
we
set
u=g(x),
then
 can
be
solved
by
the
subsCtuCon
u
=
g(x)

 





























du
=
g’(x)
dx
 and
the
integral




f(g(x))
g’(x)
dx


becomes




f(u)
du
 u
 du
 =g(x)
 f(g(x))
g’(x)
dx
=



f(u)
du

=

F(u)
+
C
=

F(g(x))
+
C

 =u 
 =du
 pick
an
an'deriva've

 [Q]
The
Subs&tu&on
rule
for
integra&on
is
the
 inverse
of
 •  (a)
The
product
rule
for
differen&a&on.
 •  (b)
The
chain
rule
for
differen&a&on.
 •  (c)
Both
of
the
above.
 


The
SubsCtuCon
rule
for
integraCon
is
the
 inverse
of
t Chain
rule
 F(g(x))
 F’(g(x))
g’(x)
 Subs'tu'on
rule
 

F’(g(x))
g’(x)
dx


 F(g(x))
+
C
 There
is
only
one
 way
to
learn
the
 subsCtuCon
rule
 for
integraCon
 PRACTICE,
PRACTICE,
PRACTICE…
 SOLVING
INDEFINITE
INTEGRALS
BY
SUBSTITUTION
 compute
integral
 in
terms
of
u
 g(x)
 f(g(x))
g’(x)
dx
=



f(u)
du

=

F(u)
+
C
=

F(g(x))
+
C
 subs'tute
 u
 du/g’(x)
 back‐subs&tute
 Step
1:
Find
the
subsCtuCon

u=g(x)
 Step
2:
Find
the
differenCal

du=g’(x)
dx

and
solve
for
dx
=
du/
g’(x)
 Step
3:
SubsCtute
g(x)=u

and

dx
=
du/
g’(x)
 Step
4:
Solve
the
integral
in
terms
of
u
 Step
5:
Back‐subsCtute
u=g(x)
 The
final
answer
should
be
in
terms
of
x
 you
should
get
an
integral
that
only
depends
on
u
 SOLVING
DEFINITE
INTEGRALS
BY
SUBSTITUTION
 b
 a
 u
 du/g’(x)
 g(b)
 g(a)
 SubsCtute and
 change

 extremes
 g(b)
 g(a)
 Compute
 integral
in
 terms
of
u
 Do
NOT
 back‐subs&tute
u=g(x).
 Instead,
use
the
new
 extremes…

 f(g(x))
g’(x)
dx



=







f(u)
du




=


F(u)




=




F(g(b))
–
F(g(a))

 Step
1:
Find
the
subsCtuCon

u=g(x)
 Step
2:
Find
the
differenCal

du=g’(x)
dx

and
solve
for
dx
=
du/
g’(x)
 Step
3:
Find
the
new
extremes
of
integraCon
 Do
NOT
forget!
 Step
4:
SubsCtute
g(x)=u

and

dx
=
du/
g’(x)
and

change
the
extremes
of
integraCon
 Step
5:
Find
an
anCderivaCve
(in
terms
of
u)
 Step
6:
Plug
in
the
new
extremes
of
integraCon
(and
take
the
difference)
 ...
View Full Document

This note was uploaded on 12/07/2010 for the course MATH MATH 2B taught by Professor Famiglietti,c during the Fall '09 term at UC Irvine.

Ask a homework question - tutors are online