L /0.. ;J S L{ 5

I I r ,

- S~f\~: Ll( q, ..?Ba ( :s \. (Skip t:nor 8ouxJ\ 3:s (S~ip Error' Boo..nd)

I

Sv ff. :2.J.\<A. S\rn~\i~ arcl uJDte II)

(~ + t)5

. 50 i

~pr. :2, J,.J- , We. \znex,0 -k'la+- (O~?r\):: ~ + ~co<; ()x). Use th~ , Y( tOh()()~hif> b h.U02 VI -Hw S ;f\£ J COS;N> orld e'x-fCnan-hoI : ~Anc-hO(\~ -6 Q):f"1~C (C,~ .. :, ( ~) as 0. / sum D+­

SIf\QS dl''\d CO'S\(\QS.

(Os. x :::::

e ­

l1t e -­

COS IT' -­--- - ( I S,1r) Tf ::::: 0 ':;0

/

'Nha+ Ore

. ~ comr~'

;!-/3i __ [.?-'( :i;i) e (' If

e"'{cOS(3)+ [Sines))

-2 ;;;J / )Ce ('05.3) of (". e s'ln lS 21hus :,ceo e cos (::,), ~= ""Sin(S). I

I I I I I I I I I I I I I I

Tr\ 0'(&( -\0 \.J..~ U)~o+- (A)e.- have. k n (Qf.b) )(

Ul~ Y\Q!?ct \1) e \f\ 0 sl.{ilob~~-\'I/.(1J\ / 3e.\­c:­

, ml- '=>0 6 b SQ.l(ve. +ho-t Co+ib)x ox lb )(

e.- -- .e.. • e,

, ~\t\\ \ ex­

=0 [(b r)t t (t-C)j--t (s r)j 1-\>: eHrllc)t 1,/:::;: N~ il)bOC\ . \ ~

~)j-t('dC)K t(6)'[he t (h-c}tC t \ cr) Jt' t (C)j ] ~: = 1'J1­. . . I

XI.J, '.)(,ur c(' -\ = \ ><jt s = N Xf ~ J 10 ',. t

hh<Z:OC '\ ~ ~ r(6 1 (c£ ) (-Cf )

L ~lJJ -t ~fJ 1-\ Ji\\ j

+ (*)t t (~)J -t\~)~ t \ ~~)t +(':) 1] 0 ~"I ~ NW co

S()()9 \' \ z

i • L(~)J t\~}tCT(~")Ji7{~)SC T(:) Jet \~1j'( -1-(~}KT(jtt)jr T (0) J ] ,,~_c = N1­

f

..:J'-::=. \. >() j-9 ;: N ><f ...:J-\J! <;. .. . Q\ 9~~ h \ t

-?"\OJIf\JI N jO ih"\'O/\ o\'tt >~

~w PIJ'O "'j... dt'O\\'}'Jlw 'b I t f>UO h' \ . t sO"\)~J 1J.r: . l

,

t. \. :2 ~ (0), Co\culQte. T~ .rCtt~ ~ i n~e5'(a. \

T~ j: / Jx

js I~ ~o \aY<j~ or -bo <Jy'o\\~ EXf\O\f\ 3\,oph,co\lj­

; ~(x)=:x ~

To, = )2-~ [ { ( ()) 4- )-\-( +) 4- lft~)+:lr(\) 4- ~(+) i Jft~)~I(;)1 .~ ~. \ II \ \

T0 i~ -\no \OYJ~ . S-\nd-\j ~O~n'\o.-h(n\ \J sf(lo~\n31-"",5. 15, ~cGtuse tlx) ~ )( S I:' COncaVE'. up on

, [0

I )1. \-\o~vQJ' I J~a~h·\c.a\ \ j we.. CO-f\ 'SefL i+ a'S tll6lO!I:

Til tXe-t(ises 3\ a.nd

0,,- NlN un cl.e y (' S -h t1\Q k.s 33 stote wh.+fte , I<\):fltf3raI (b~t do' t1tr+ Or ) oveYRS.J-;fha+e, ~

caleu[a-k' T;J Or MN

) .

1;0

3\IIIV'J ~tevyy\i~n l< )" - -l e -" I~

r;'''(,,) '" i q

e -'/~

-4te R~ pDr\Qn +io \ -J''' (>.) , 0 ~Y' a 11

x ._ h OILU~S p.,S,h"",Oil oil 0+' IR

I SIn", +v is COI'\(ave.

\ ;rIo; (os X OWX{:>t;rnates ~ in).e3ral . Jo

WI(_ L{'5.e. -ftte :sa tr\Q~(x):::: CDS~ ~n InI 31. T-C

~'(x)-::::: -si~x

+' "(A):::: ­ (0:, X

[ 0, "TJ /.., ] f (O~ X

I') posi-hv€,~ is C()0(Qve

OV0rQ s-h rna+e douJl') . Th i :., or"~ ()() < 0 and fY\eOJ1S~ 'nk:ra \. ~(J+- M:>o

[Xe¥i' '\ ':;(''3> l .J _\'3 h eva\uo\e

J\ f!.-x ~'nx

LA.. =- sin X

, \J = .(tJ::' x

" -'/V ::- e

-x V :- - e

! -x -e. ~ e-> ~\nx J~)+~- e Cos ><

_ x _ )<

== - e (os X - e S 1,(\ X je- X $\(\xdX

). j e '-Y S\\,\X ~x ::. - Q -x C<X, X -- e-)( S\r\)( +- C

[) e~X si!\i( ~. ". ~ e·' ( COSi( + sin x')-:t]

V ,

:= d/<

\j= _\ )X in?­

"Tn [x0.l'iSQs

Q \JQ \v.o.1{( LAS, rj 0'<' b()~l J',

1. J. 3to

== ),{Ln u c1J

= Ift~ lA - V. -\ C (Yf! E"""'f\. \ r qJ~)

=~~~ )Un (in x)) - !"x ~ eJ

1- . .J . 3'9 S CD')( J.n ls.n,) J.X

V\.= sin X -) ~ -= (0$><" -Q c\x =- ~ ~ Cmx

- . \' CO~ x J,n (S'lf'I;>') ~. := \ Co~ x J-n Ll . sJ)JJ J Cos x

cc jto (j eVA

-=- ulv"-A - LA + C

== ~:i~:j~~}) ~ ~~~;~-g

1.J.4:1­

\IV w v~ e -) V=e

\ W V'J V -=- e -~ V-s::e ,

.. j..r,: €..r,. Jx "" }v/evJ ~ ('1 VIle'" _ SL\e. W dw )

, V :: )<

U. ::: x:l-l-\

j" -lo'; \ J,y ="

t~QY[I::.e~ 1.) . ~I(q

i f\ tP5t'o\ .

, , u-= ~r\x

- \ \.A

'\

- - v = x ><

~ \" JI' x J, x = d i'» \ ~ ~ j ,0; J x

,,- lx In x- >r =c (3~" OS - :s) - ( 0 - I) ~~-~

l J ll1

(\JO\lAO\e. S)!. f\ L" xdx I-tw Y' =f -- \ _

0\'()\j\ c\ be. u';)ed tn evolvoJe

We. Con ~'~ lA -- ~ I)bst~v,\\on -b (]\io\vofe --S A- \ltl >c- Jx As ~- -tk Cc\SQ. (\4-\ , 10~ ~-\(\ye.

, 0LA::: lv\ x v :: X

\'"1+\\ ;x-\). \

-" \/-.::x n¥ \

L

E:"o\v.o.\~ S&in- 'x)..:1 Jx . \-\~~ . U<se. "Tn'\f3yotlol') 6j Po-As Gnd -\-\\Qf\ s\Abs-h~l.\hol'\ .

'NIL hv~t U~ In~~jYatlO'" b~ \)Oy'+s '.

u = (0,;,,- \)( r v :::. I

V7 X

, v =- 'S'\n~ ) v=- -- Co~ U

}

\: ) 5 \ fI- I )(.. -j! ;) d"X ::: -;)u (OS U -+ \ ;Jco~ U dA,J,J ~'JI-~ J

,?\ lA~~\ Y\q -,,\;',s 'cu<.k. ~ ~ei-

SCSi~-' li)'" d.x -= xC,,;;,,-\ r L- )LlCOSU -\- )",i" uJ -l- C

== )< l ;,i,,- 'xY'+ )5i,,-' li (=( )in-' x) - ;:l sin Lsin- 'x)~ c ~x -rl-x~ =8 s't'-'xY -\ )<;.;')( ( 0) - :lx~ C~ ...;

(OS G :: (0'S (~0'\)~ n

J;"d fC,,), Q"S~""~3 .Iha-l-

JH~) Q'" ct" '" HA)e x 5\.'" "d>< Here

have \A :::: rC ~ ~ , LJeS"d) and v -. :>( ]'n·lP3ro·h On

Y),usl e . 6:; ~y\ho.ve SillCQ v wM1-l-h a+ \

I::' +l\Qxel6(Q "" ::::LA -f(A) :=

e / We-XSo +t'd+ +CA] -:::­ S \Ix ::::­ in x +( +tir

'SoI'Y\Q COIj~-hr\ t C.