12 x1 t05 05 integration with inverse trig (2013)
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Transcript of 12 x1 t05 05 integration with inverse trig (2013)
![Page 1: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/1.jpg)
Integration Involving Inverse Trig
![Page 2: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/2.jpg)
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin
![Page 3: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/3.jpg)
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin OR c
ax
1cos
![Page 4: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/4.jpg)
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin OR c
ax
1cos
22 xadx c
ax
a
1tan1
![Page 5: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/5.jpg)
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin OR c
ax
1cos
22 xadx c
ax
a
1tan1
e.g. 24 x
dxi
![Page 6: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/6.jpg)
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin OR c
ax
1cos
22 xadx c
ax
a
1tan1
e.g. 24 x
dxi
cx
2sin 1
![Page 7: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/7.jpg)
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin OR c
ax
1cos
22 xadx c
ax
a
1tan1
e.g. 24 x
dxi
cx
2sin 1
29 xdxii
![Page 8: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/8.jpg)
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin OR c
ax
1cos
22 xadx c
ax
a
1tan1
e.g. 24 x
dxi
cx
2sin 1
29 xdxii
cx
3tan
31 1
![Page 9: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/9.jpg)
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin OR c
ax
1cos
22 xadx c
ax
a
1tan1
e.g. 24 x
dxi
cx
2sin 1
29 xdxii
cx
3tan
31 1
1
022 x
dxiii
![Page 10: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/10.jpg)
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin OR c
ax
1cos
22 xadx c
ax
a
1tan1
e.g. 24 x
dxi
cx
2sin 1
29 xdxii
cx
3tan
31 1
1
022 x
dxiii1
0
1
2sin
x
![Page 11: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/11.jpg)
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin OR c
ax
1cos
22 xadx c
ax
a
1tan1
e.g. 24 x
dxi
cx
2sin 1
29 xdxii
cx
3tan
31 1
1
022 x
dxiii1
0
1
2sin
x
0sin2
1sin 11
![Page 12: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/12.jpg)
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin OR c
ax
1cos
22 xadx c
ax
a
1tan1
e.g. 24 x
dxi
cx
2sin 1
29 xdxii
cx
3tan
31 1
1
022 x
dxiii1
0
1
2sin
x
0sin2
1sin 11
4
04
![Page 13: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/13.jpg)
0
2log2
1
1 evaluate hence and sin Find dx
eee
dxdiv
x
xx
![Page 14: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/14.jpg)
0
2log2
1
1 evaluate hence and sin Find dx
eee
dxdiv
x
xx
xedxd 1sin
x
x
ee
21
![Page 15: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/15.jpg)
0
2log2
1
1 evaluate hence and sin Find dx
eee
dxdiv
x
xx
xedxd 1sin
x
x
ee
21
0 2log1
0
2log2
sin1
xx
x
edxe
e
![Page 16: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/16.jpg)
0
2log2
1
1 evaluate hence and sin Find dx
eee
dxdiv
x
xx
xedxd 1sin
x
x
ee
21
0 2log1
0
2log2
sin1
xx
x
edxe
e
3
62
21sin1sin
sinsin
11
2log101
ee
![Page 17: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/17.jpg)
0
2log2
1
1 evaluate hence and sin Find dx
eee
dxdiv
x
xx
xedxd 1sin
x
x
ee
21
0 2log1
0
2log2
sin1
xx
x
edxe
e
3
62
21sin1sin
sinsin
11
2log101
ee
294 xdxv
![Page 18: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/18.jpg)
0
2log2
1
1 evaluate hence and sin Find dx
eee
dxdiv
x
xx
xedxd 1sin
x
x
ee
21
0 2log1
0
2log2
sin1
xx
x
edxe
e
3
62
21sin1sin
sinsin
11
2log101
ee
294 xdxv
2
943 x
dx
![Page 19: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/19.jpg)
0
2log2
1
1 evaluate hence and sin Find dx
eee
dxdiv
x
xx
xedxd 1sin
x
x
ee
21
0 2log1
0
2log2
sin1
xx
x
edxe
e
3
62
21sin1sin
sinsin
11
2log101
ee
294 xdxv
2
943 x
dx
2
943
1
x
dx
![Page 20: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/20.jpg)
0
2log2
1
1 evaluate hence and sin Find dx
eee
dxdiv
x
xx
xedxd 1sin
x
x
ee
21
0 2log1
0
2log2
sin1
xx
x
edxe
e
3
62
21sin1sin
sinsin
11
2log101
ee
294 xdxv
2
943 x
dx
2
943
1
x
dx
cx
23sin
31 1
![Page 21: 12 x1 t05 05 integration with inverse trig (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052622/5591a1bb1a28abae268b4700/html5/thumbnails/21.jpg)
0
2log2
1
1 evaluate hence and sin Find dx
eee
dxdiv
x
xx
xedxd 1sin
x
x
ee
21
0 2log1
0
2log2
sin1
xx
x
edxe
e
3
62
21sin1sin
sinsin
11
2log101
ee
294 xdxv
2
943 x
dx
2
943
1
x
dx
cx
23sin
31 1
Exercise 1E; 2, 3, 4a, 5b, 6 & 7bdf, 9,12, 13, 16, 17, 20, 22