12x1 t02 02 integrating exponentials
TRANSCRIPT
Integrating Exponentials
Integrating Exponentials
dxeax
Integrating Exponentials
dxeax cea
ax 1
Integrating Exponentials
dxeax cea
ax 1
dxexf xf
Integrating Exponentials
dxeax cea
ax 1
dxexf xf ce xf
Integrating Exponentials
dxeax cea
ax 1
dxexf xf ce xf
dxei x5 e.g.
Integrating Exponentials
dxeax cea
ax 1
dxexf xf ce xf
dxei x5 e.g.
ce x 5
51
Integrating Exponentials
dxeax cea
ax 1
dxexf xf ce xf
dxei x5 e.g.
ce x 5
51
dxe
dxe
x
x
5
5
551
OR
Integrating Exponentials
dxeax cea
ax 1
dxexf xf ce xf
dxei x5 e.g.
ce x 5
51
dxe
dxe
x
x
5
5
551
ce x 5
51
OR
dxxeii x2
dxxeii x2
dxxex2
221
dxxeii x2
dxxex2
221
cex 2
21
dxxeii x2
dxxex2
221
cex 2
21
dxeiii x 59 dxe x 59991
dxxeii x2
dxxex2
221
cex 2
21
dxeiii x 59 dxe x 59991
ce x 59
91
dxxeii x2
dxxex2
221
cex 2
21
dxeiii x 59 dxe x 59991
dxe iv x
ce x 59
91
dxxeii x2
dxxex2
221
cex 2
21
dxeiii x 59 dxe x 59991
dxe iv x dxex2
ce x 59
91
dxxeii x2
dxxex2
221
cex 2
21
dxeiii x 59 dxe x 59991
dxe iv x dxex2
dxex2
212
ce x 59
91
dxxeii x2
dxxex2
221
cex 2
21
dxeiii x 59 dxe x 59991
dxe iv x dxex2
dxex2
212
ce x 59
91
ce
cex
x
2
2 2
dxxeii x2
dxxex2
221
cex 2
21
dxeiii x 59 dxe x 59991
dxe iv x dxex2
dxex2
212
ce x 59
91
ce
cex
x
2
2 2
dxee v xx 31
dxxeii x2
dxxex2
221
cex 2
21
dxeiii x 59 dxe x 59991
dxe iv x dxex2
dxex2
212
ce x 59
91
ce
cex
x
2
2 2
dxee v xx 31
dxee xx 322
dxxeii x2
dxxex2
221
cex 2
21
dxeiii x 59 dxe x 59991
dxe iv x dxex2
dxex2
212
ce x 59
91
ce
cex
x
2
2 2
dxee v xx 31
dxee xx 322
cxee xx 3221 2
dxxeii x2
dxxex2
221
cex 2
21
dxeiii x 59 dxe x 59991
dxe iv x dxex2
dxex2
212
ce x 59
91
ce
cex
x
2
2 2
dxee v xx 31
dxee xx 322
cxee xx 3221 2
dx
eee vi x
xx
2
5
dxxeii x2
dxxex2
221
cex 2
21
dxeiii x 59 dxe x 59991
dxe iv x dxex2
dxex2
212
ce x 59
91
ce
cex
x
2
2 2
dxee v xx 31
dxee xx 322
cxee xx 3221 2
dx
eee vi x
xx
2
5
dxee xx3
dxxeii x2
dxxex2
221
cex 2
21
dxeiii x 59 dxe x 59991
dxe iv x dxex2
dxex2
212
ce x 59
91
ce
cex
x
2
2 2
dxee v xx 31
dxee xx 322
cxee xx 3221 2
dx
eee vi x
xx
2
5
dxee xx3
cee xx 3
31
dxexvii x1
0
2 3
dxexvii x1
0
2 3
dxex x1
0
2 3
331
103
31 xe
dxexvii x1
0
2 3
dxex x1
0
2 3
331
103
31 xe
dxexvii x1
0
2 3
01
31 ee
dxex x1
0
2 3
331
103
31 xe
dxexvii x1
0
2 3
01
31 ee
131
e
dxex x1
0
2 3
331
103
31 xe
dxexvii x1
0
2 3
01
31 ee
dx viii x3
131
e
dxex x1
0
2 3
331
103
31 xe
dxexvii x1
0
2 3
01
31 ee
dx viii x3
cx
3log
3
131
e
dxex x1
0
2 3
331
103
31 xe
Exercise 13C; 2 to 8 ace etc, 9, 10,11, 13, 17
Exercise 13D; 2 to 18 evens, 21*
dxexvii x1
0
2 3
01
31 ee
dx viii x3
cx
3log
3
131
e
dxex x1
0
2 3
331