12x1 t05 05 integration with inverse trig (2010)

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