12 x1 t01 03 integrating derivative on function (2013)

Integrating Derivative on Function

Integrating Derivative on Function

dxxfxf cxf log

Integrating Derivative on Function

dxxfxf cxf log

e.g. (i) dx

x371

Integrating Derivative on Function

dxxfxf cxf log

e.g. (i) dx

x371

dxx37

331

Integrating Derivative on Function

dxxfxf cxf log

e.g. (i) dx

x371

dxx37

331

cx 37log31

Integrating Derivative on Function

dxxfxf cxf log

e.g. (i) dx

x371

dxx37

331

58

xdxii

cx 37log31

Integrating Derivative on Function

dxxfxf cxf log

e.g. (i) dx

x371

dxx37

331

58

xdxii

588

81

xdx

cx 37log31

Integrating Derivative on Function

dxxfxf cxf log

e.g. (i) dx

x371

dxx37

331

58

xdxii

588

81

xdx

cx 58log81 cx 37log

31

Integrating Derivative on Function

dxxfxf cxf log

e.g. (i) dx

x371

dxx37

331

58

xdxii

588

81

xdx

cx 58log81

dx

xxiii

2 6

5

cx 37log31

Integrating Derivative on Function

dxxfxf cxf log

e.g. (i) dx

x371

dxx37

331

58

xdxii

588

81

xdx

cx 58log81

dx

xxiii

2 6

5

dx

xx

26

61

6

5

cx 37log31

Integrating Derivative on Function

dxxfxf cxf log

e.g. (i) dx

x371

dxx37

331

58

xdxii

588

81

xdx

cx 58log81

dx

xxiii

2 6

5

cx 2log61 6

dx

xx

26

61

6

5

cx 37log31

dxx

iv51

dxx

iv51

dxx5

551

dxx

iv51

dxx5

551

cx 5log51

dxx

iv51

dxx5

551

cx 5log51

OR dxx1

51

dxx

iv51

dxx5

551

cx 5log51

OR dxx1

51

cx log51

dxx

iv51

dxx5

551

cx 5log51

OR dxx1

51

cx log51

dx

xx v

1214

dxx

iv51

dxx5

551

cx 5log51

OR dxx1

51

cx log51

dx

xx v

1214 rdenominatoorder numeratororder

dxx

iv51

dxx5

551

cx 5log51

OR dxx1

51

cx log51

dx

xx v

1214 rdenominatoorder numeratororder

divisionpolynomial

dxx

iv51

dxx5

551

cx 5log51

OR dxx1

51

cx log51

dx

xx v

1214 rdenominatoorder numeratororder

divisionpolynomial

124

21412

xxx

dxx

iv51

dxx5

551

cx 5log51

OR dxx1

51

cx log51

dx

xx v

1214 rdenominatoorder numeratororder

divisionpolynomial

124

21412

xxx

dx

x 1212

dxx

iv51

dxx5

551

cx 5log51

OR dxx1

51

cx log51

dx

xx v

1214 rdenominatoorder numeratororder

divisionpolynomial

124

21412

xxx

dx

x 1212

cxx 12log212

dxx

xvi

2

12 12

212 1log x

dxx

xvi

2

12 12

212 1log x

dxx

xvi

2

12 12

2log5log

212 1log x

dxx

xvi

2

12 12

2log5log

25log

212 1log x

dxx

xvi

2

12 12

2log5log

xx

xx viilog integrate

hence and log ateDifferenti 2

3

25log

212 1log x

dxx

xvi

2

12 12

2log5log

xx

xx viilog integrate

hence and log ateDifferenti 2

3

233 3log1log xxx

xxxdxd

25log

212 1log x

dxx

xvi

2

12 12

2log5log

xx

xx viilog integrate

hence and log ateDifferenti 2

3

233 3log1log xxx

xxxdxd

xxx log3 22

25log

212 1log x

dxx

xvi

2

12 12

2log5log

xx

xx viilog integrate

hence and log ateDifferenti 2

3

233 3log1log xxx

xxxdxd

xxx log3 22

25log cxxdxxxx loglog3 322

212 1log x

dxx

xvi

2

12 12

2log5log

xx

xx viilog integrate

hence and log ateDifferenti 2

3

233 3log1log xxx

xxxdxd

xxx log3 22

25log cxxdxxxx loglog3 322

cdxxxxdxxx 232 loglog3

212 1log x

dxx

xvi

2

12 12

2log5log

xx

xx viilog integrate

hence and log ateDifferenti 2

3

233 3log1log xxx

xxxdxd

xxx log3 22

25log cxxdxxxx loglog3 322

cdxxxxdxxx 232 loglog3

cxxxdxxx 332

91log

31log

212 1log x

Exercise 12D; 1 to 12 ace in all, 14a*

Exercise 12E; 1 to 6 all, 7 to 21 odds, 22abc*, 23*

dxx

xvi

2

12 12

2log5log

xx

xx viilog integrate

hence and log ateDifferenti 2

3

233 3log1log xxx

xxxdxd

xxx log3 22

25log cxxdxxxx loglog3 322

cdxxxxdxxx 232 loglog3

cxxxdxxx 332

91log

31log