12x1 t03 04 integrating trig (2011)

Integrating Trig

Integrating Trig dxbaxcos

Integrating Trig dxbaxcos cbax

a sin1

Integrating Trig dxbaxcos cbax

a sin1

sin dxbax

Integrating Trig dxbaxcos cbax

a sin1

sin dxbax cbaxa

cos1

Integrating Trig dxbaxcos cbax

a sin1

sin dxbax cbaxa

cos1

dxbax2sec

Integrating Trig dxbaxcos cbax

a sin1

sin dxbax cbaxa

cos1

dxbax2sec cbaxa

tan1

Integrating Trig dxbaxcos cbax

a sin1

sin dxbax cbaxa

cos1

dxbax2sec cbaxa

tan1

xdxi 3sin e.g.

Integrating Trig dxbaxcos cbax

a sin1

sin dxbax cbaxa

cos1

dxbax2sec cbaxa

tan1

xdxi 3sin e.g. cx 3cos31

Integrating Trig dxbaxcos cbax

a sin1

sin dxbax cbaxa

cos1

dxbax2sec cbaxa

tan1

xdxi 3sin e.g. cx 3cos31

dxxii 51cos

Integrating Trig dxbaxcos cbax

a sin1

sin dxbax cbaxa

cos1

dxbax2sec cbaxa

tan1

xdxi 3sin e.g. cx 3cos31

dxxii 51cos cx 51sin51

Integrating Trig dxbaxcos cbax

a sin1

sin dxbax cbaxa

cos1

dxbax2sec cbaxa

tan1

xdxi 3sin e.g. cx 3cos31

dxxii 51cos cx 51sin51

dxxiii

2sec 2

Integrating Trig dxbaxcos cbax

a sin1

sin dxbax cbaxa

cos1

dxbax2sec cbaxa

tan1

xdxi 3sin e.g. cx 3cos31

dxxii 51cos cx 51sin51

dxxiii

2sec 2 cx

2tan2

2

6

2sin

xdxiv

2

6

2sin

xdxiv2

6

2cos21

x

2

6

2sin

xdxiv2

6

2cos21

x

3coscos

21

2

6

2sin

xdxiv2

6

2cos21

x

3coscos

21

43

211

21

2

6

2sin

xdxiv2

6

2cos21

x

3coscos

21

43

211

21

axis.thearoundrotatedis1 and 0between sin when

formedsolidtheofvolume theFind

xxxxy

v

2

6

2sin

xdxiv2

6

2cos21

x

3coscos

21

43

211

21

axis.thearoundrotatedis1 and 0between sin when

formedsolidtheofvolume theFind

xxxxy

v

1

0

2

sin xdx

dxyV

2

6

2sin

xdxiv2

6

2cos21

x

3coscos

21

43

211

21

axis.thearoundrotatedis1 and 0between sin when

formedsolidtheofvolume theFind

xxxxy

v

1

0

2

sin xdx

dxyV

1

0

cos1

x

2

6

2sin

xdxiv2

6

2cos21

x

3coscos

21

43

211

21

axis.thearoundrotatedis1 and 0between sin when

formedsolidtheofvolume theFind

xxxxy

v

1

0

2

sin xdx

dxyV

1

0

cos1

x

3units211

0coscos

2

6

2sin

xdxiv2

6

2cos21

x

3coscos

21

43

211

21

axis.thearoundrotatedis1 and 0between sin when

formedsolidtheofvolume theFind

xxxxy

v

1

0

2

sin xdx

dxyV

1

0

cos1

x

3units211

0coscos

dxxxvi 22sec

2

6

2sin

xdxiv2

6

2cos21

x

3coscos

21

43

211

21

axis.thearoundrotatedis1 and 0between sin when

formedsolidtheofvolume theFind

xxxxy

v

1

0

2

sin xdx

dxyV

1

0

cos1

x

3units211

0coscos

dxxxvi 22sec dxxx 22sec221

2

6

2sin

xdxiv2

6

2cos21

x

3coscos

21

43

211

21

axis.thearoundrotatedis1 and 0between sin when

formedsolidtheofvolume theFind

xxxxy

v

1

0

2

sin xdx

dxyV

1

0

cos1

x

3units211

0coscos

dxxxvi 22sec dxxx 22sec221

cx 2tan21

xdxvii 2sin

xdxvii 2sin cos2

xdxvii 2sin cos2 22 sincos

xdxvii 2sin cos2 22 sincos 2cos1

21sinsin21 22

xdxvii 2sin cos2 22 sincos 2cos1

21sinsin21 22

2cos121cos1cos2 22

xdxvii 2sin cos2 22 sincos 2cos1

21sinsin21 22

2cos121cos1cos2 22

dxx2cos121

xdxvii 2sin cos2 22 sincos 2cos1

21sinsin21 22

2cos121cos1cos2 22

dxx2cos121

cxx

cxx

2sin41

2

2sin21

21

xdxvii 2sin cos2 22 sincos 2cos1

21sinsin21 22

2cos121cos1cos2 22

dxx2cos121

cxx

cxx

2sin41

2

2sin21

21

xdxvii tan

xdxvii 2sin cos2 22 sincos 2cos1

21sinsin21 22

2cos121cos1cos2 22

dxx2cos121

cxx

cxx

2sin41

2

2sin21

21

xdxvii tan dxxx

cossin

xdxvii 2sin cos2 22 sincos 2cos1

21sinsin21 22

2cos121cos1cos2 22

dxx2cos121

cxx

cxx

2sin41

2

2sin21

21

xdxvii tan dxxx

cossin

dxxx

cossin

xdxvii 2sin cos2 22 sincos 2cos1

21sinsin21 22

2cos121cos1cos2 22

dxx2cos121

cxx

cxx

2sin41

2

2sin21

21

xdxvii tan dxxx

cossin

dxxx

cossin

cx coslog

xdxvii 2sin cos2 22 sincos 2cos1

21sinsin21 22

2cos121cos1cos2 22

dxx2cos121

cxx

cxx

2sin41

2

2sin21

21

xdxvii tan dxxx

cossin

dxxx

cossin

cx coslog

cx

cx

seclogcoslog 1

xdxxix

π

72

0

sincos

xdxxix

π

72

0

sincos xu sin

xdxxix

π

72

0

sincos xu sinxdxdu cos

xdxxix

π

72

0

sincos xu sinxdxdu cos

1,2

00

ux

,ux

xdxxix

π

72

0

sincos xu sinxdxdu cos

1,2

00

ux

,ux

1

0

7duu

xdxxix

π

72

0

sincos xu sinxdxdu cos

1,2

00

ux

,ux

1

0

7duu 1

0

8

81

u

xdxxix

π

72

0

sincos xu sinxdxdu cos

1,2

00

ux

,ux

1

0

7duu 1

0

8

81

u

81

0181 8

Exercise 14I; 2ace etc, 3ace etc, 4, 6, 8a, 9ac, 10a, 12ace, 13b(i), 14df, 15ace

Exercise 14J; 2b, 3bfh, 4a, 5ac, 7, 9, 10, 13, 14, 21, 26

xdxxix

π

72

0

sincos xu sinxdxdu cos

1,2

00

ux

,ux

1

0

7duu 1

0

8

81

u

81

0181 8