# MAT136H1 Lecture Notes - Lecture 5: Inverse Trigonometric Functions, Institute Of Directors, Telephone Numbers In France

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3 Feb 2016
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27/or r/ t C'
{o
{nc (echninue o F )vbSti tvtion or Chan;e o{ Variable
-F; "d f{c*} a>" :
' Example 7
" Finl -f rot Lsz) az-
" Solu4ion
/c+ u = 5x'
{hen i? = S
d'c
5o clv . 5x and dz = tau
H enc s -f,..t6ia*
= fGos u) (A a*)
tr^
= €.1 cost-td*
I
-- -?<ir-t(,t + C
€s,"(S-) + C
'tao,rnpl€ Z
o Fiod .[C, * + t)z"o dx-
' So lu* ion
./z+ p7= /2a + I
-i'h"" /7ez = ?
f o /v - 1a Y. ctnJ &t' lz du
l4enc.e / Czrc+ t):oo "{Y
= -fu"-" (t)du
=/z (*)r c
, .: 2ol
(2-x+t) , -
l+o 4
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Remark - i{an inie3rc,lion ?roble- r'5 ,*o " a}[s 4id
using s)"npty +he iubs'fi+ul io, @ "rF;ZV1A
C,-ohert €L r' nd b ^r€ Conslctrr-i"s) t frou sheuli be aple t"
atrile clowr, lt--',e {;nq! anttr€r imrt€dfate;g
Exo,n pl es
" 4J6x4 * =
" -f , t. (+) dy - -fP = -t1,c*,, ((1 + c
(z- az) + c
exa-7te 3f oQ)t*2
of;n4 J ffidz
e Solv-tt'cn-
f 92cc+2
-/ G,.z .trc
,o i€x
Erc
( ,* te4l;"3
\ nene. d u
arclan u + C
a rc|",n ( ato') r C
-*+o^
*6
= ez f '{^t **
,/ I + eL+:c
,/' t
oz / €dtl
ll 1-
-/ l+oZ
cz t dut
1J t+u1
t;-= 812 \
= Zcrz.t= )
e"
2
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