# MAT136H1 Lecture Notes - Lecture 1: Antiderivative, File Exchange Protocol, Inverse Trigonometric Functions

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3 Feb 2016
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Ant ideri"rative :
'De€;n;(;on - Aftnct'on fb) 5uch4ha-t F'(>r,)- {bc> r'3
ca-lls4 an an(rrterivc+tivet o€ €Cd t
' EX ami> ie
" .* ?C? - 3x<
d7'
l4enee 3xi is -l-h e deri va'live c>F XP
1)snc e 2c< is the c.nt r'cleri vqlive o{ 3>c<
' fioLe tyr"t 2L3 + | is anolher antidgriv&+|rs o€
3z< , since *. (zt*t) = 3z-1
o 5 i.ni lcu"; 0., za * Z ; t Ael ano*her an+;c1e-ivc.-tivc,
o( 3sca, since **C*znil-37R
"IoA'€nerc^\ ,23+C (uhete. C r's ^r1 ar^5,'tra-ry
constanL) r-5 an a,nl,derir6nlive- ol 3>z,sioce
*o (rt *.) -- j:r<
R-e,-rorl< - 5^ Ae"tere^l , ,'F F(z) r^ 3
oF Ffz)r-fhen l:(>c)+L Cr.thereC
\3/o | / tG
ar1 an Li de riwa*i ve
,'t an a' r^ b i {r c^. t4
o€ {C-) or4Ae ol flC>c) and
a-,ill ba dcnoled by *he sgrnbot jr*)a*
cat\ed the iolegral
is calt ed dn iat ea ro,lion 4ormul a,
_
oeeds to \$;.np t 7
{o prov& €vc.h c* €orrnr;l 6- r orle
s ho ru 4h a.* -Lo* tr[>c) = fcx)
f,o o*her p,,2ords7 JfaSd.r= f(x)+6 ?-> \$fCx)-- {ir.)
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