12 x1 t02 02 integrating exponentials (2014)

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