12x1 t05 05 integration with inverse trig (2010)
TRANSCRIPT
Integration Involving Inverse Trig
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin OR c
ax
1cos
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin OR c
ax
1cos
22 xadx c
ax
a
1tan1
Integration Involving Inverse Trig
22 xa
dxc
ax
1sin OR c
ax
1cos
22 xadx c
ax
a
1tan1
e.g. 24 x
dxi
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
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
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
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
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
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
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
0
2log2
1
1 evaluate hence and sin Find dx
eee
dxdiv
x
xx
0
2log2
1
1 evaluate hence and sin Find dx
eee
dxdiv
x
xx
xedxd 1sin
x
x
ee
21
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
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
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
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
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
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
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