12x1 t03 04 integrating trig functions
TRANSCRIPT
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Integrating Trig
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Integrating Trig dxbaxcos
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Integrating Trig dxbaxcos cbax
a sin1
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Integrating Trig dxbaxcos cbax
a sin1
sin dxbax
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Integrating Trig dxbaxcos cbax
a sin1
sin dxbax cbaxa
cos1
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Integrating Trig dxbaxcos cbax
a sin1
sin dxbax cbaxa
cos1
dxbax2sec
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Integrating Trig dxbaxcos cbax
a sin1
sin dxbax cbaxa
cos1
dxbax2sec cbaxa
tan1
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Integrating Trig dxbaxcos cbax
a sin1
sin dxbax cbaxa
cos1
dxbax2sec cbaxa
tan1
xdxi 3sin e.g.
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Integrating Trig dxbaxcos cbax
a sin1
sin dxbax cbaxa
cos1
dxbax2sec cbaxa
tan1
xdxi 3sin e.g. cx 3cos31
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Integrating Trig dxbaxcos cbax
a sin1
sin dxbax cbaxa
cos1
dxbax2sec cbaxa
tan1
xdxi 3sin e.g. cx 3cos31
dxxii 51cos
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Integrating Trig dxbaxcos cbax
a sin1
sin dxbax cbaxa
cos1
dxbax2sec cbaxa
tan1
xdxi 3sin e.g. cx 3cos31
dxxii 51cos cx 51sin51
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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
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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
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2
6
2sin
xdxiv
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2
6
2sin
xdxiv2
6
2cos21
x
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2
6
2sin
xdxiv2
6
2cos21
x
3coscos
21
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2
6
2sin
xdxiv2
6
2cos21
x
3coscos
21
43
211
21
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2
6
2sin
xdxiv2
6
2cos21
x
3coscos
21
43
211
21
axis.thearoundrotatedis1 and 0between sin when
formedsolidtheofvolume theFind
xxxxy
v
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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
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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
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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
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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
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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
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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
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xdxvii 2sin
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xdxvii 2sin cos2
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xdxvii 2sin cos2 22 sincos
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xdxvii 2sin cos2 22 sincos 2cos1
21sinsin21 22
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xdxvii 2sin cos2 22 sincos 2cos1
21sinsin21 22
2cos121cos1cos2 22
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xdxvii 2sin cos2 22 sincos 2cos1
21sinsin21 22
2cos121cos1cos2 22
dxx2cos121
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xdxvii 2sin cos2 22 sincos 2cos1
21sinsin21 22
2cos121cos1cos2 22
dxx2cos121
cxx
cxx
2sin41
2
2sin21
21
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xdxvii 2sin cos2 22 sincos 2cos1
21sinsin21 22
2cos121cos1cos2 22
dxx2cos121
cxx
cxx
2sin41
2
2sin21
21
xdxvii tan
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xdxvii 2sin cos2 22 sincos 2cos1
21sinsin21 22
2cos121cos1cos2 22
dxx2cos121
cxx
cxx
2sin41
2
2sin21
21
xdxvii tan dxxx
cossin
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xdxvii 2sin cos2 22 sincos 2cos1
21sinsin21 22
2cos121cos1cos2 22
dxx2cos121
cxx
cxx
2sin41
2
2sin21
21
xdxvii tan dxxx
cossin
dxxx
cossin
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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
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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
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xdxxix
π
72
0
sincos
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xdxxix
π
72
0
sincos xu sin
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xdxxix
π
72
0
sincos xu sinxdxdu cos
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xdxxix
π
72
0
sincos xu sinxdxdu cos
1,2
00
ux
,ux
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xdxxix
π
72
0
sincos xu sinxdxdu cos
1,2
00
ux
,ux
1
0
7duu
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xdxxix
π
72
0
sincos xu sinxdxdu cos
1,2
00
ux
,ux
1
0
7duu 1
0
8
81
u
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xdxxix
π
72
0
sincos xu sinxdxdu cos
1,2
00
ux
,ux
1
0
7duu 1
0
8
81
u
81
0181 8
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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