DEFINITE INTEGRALS
b
1 b NO C
flxl.de F x F bl F a
a
Netchange of
ntegratef rst
FIXIfromato f fflxldxsff xldx.f
wax
a b
The Fundamental theorem of Calculus FTC
b
fftxldx flxl flbl f.la
m FM
l IEEEHa
Saf na FIN FIM E.f f19H9
, Fax FIX FIN flnw.hn
h EE
fffldx FIX F19411 FHY flgw.g xlflhlxy.hn
Z 1
1
x
du
0
2
(2 ¡ x )
3 dx
E
1
4
412 212
4
f El n
Z
Je
1
2
x ¢ e¡x dx
0
D
2
4 et 1 E E
calculator Allowed
Z 5
¡ ¢ d
ln x3 dx ForT nsp re
2
, Et d µZ x p ¶
1 + sin2 t ¢ dt ats n
dx ¡1
µZ 1 ¶
d 2
e¡t dt e
dx x
ÃZ !
7
x2
d 1
dt 2
dx 1 3+t 31 2
Z cos x p
F nd F.lk fFlXI 0
1 ¡ t3 dt
Z cos x pT
0
1 ¡ t3 dt
Fusx 1 s nx
Z 6 p
E Reexpress
3
x x ¡ 2dx nclud ng the boundar es
n terms of u for 4 25
7 then solve
b
1
zkf.f 2F2 42 2
duu 2 x
i
b
1 b NO C
flxl.de F x F bl F a
a
Netchange of
ntegratef rst
FIXIfromato f fflxldxsff xldx.f
wax
a b
The Fundamental theorem of Calculus FTC
b
fftxldx flxl flbl f.la
m FM
l IEEEHa
Saf na FIN FIM E.f f19H9
, Fax FIX FIN flnw.hn
h EE
fffldx FIX F19411 FHY flgw.g xlflhlxy.hn
Z 1
1
x
du
0
2
(2 ¡ x )
3 dx
E
1
4
412 212
4
f El n
Z
Je
1
2
x ¢ e¡x dx
0
D
2
4 et 1 E E
calculator Allowed
Z 5
¡ ¢ d
ln x3 dx ForT nsp re
2
, Et d µZ x p ¶
1 + sin2 t ¢ dt ats n
dx ¡1
µZ 1 ¶
d 2
e¡t dt e
dx x
ÃZ !
7
x2
d 1
dt 2
dx 1 3+t 31 2
Z cos x p
F nd F.lk fFlXI 0
1 ¡ t3 dt
Z cos x pT
0
1 ¡ t3 dt
Fusx 1 s nx
Z 6 p
E Reexpress
3
x x ¡ 2dx nclud ng the boundar es
n terms of u for 4 25
7 then solve
b
1
zkf.f 2F2 42 2
duu 2 x
i
