12 x1 t05 05 integration with inverse trig (2013)

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