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20E_Exam2B_soln

# 20E_Exam2B_soln - B MATH 1 10 EXAM 2 Please a nsv/er t he f...

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B MATH 110 EXAM #2 Please ansv/er the following questions. You wi,il not get Iess you demonstrate how you arrived at them. In short, Numerical integrations by calculator will not be accepted. cred'it for answers un- please show all work. Consider the region in the plane R : {L ( r < 2, below). IJse the change of variables fi - u, U = uu to (Hint: One of the main the (u, u) coordinates). \ I=l x=e t & {* ? d""* t + * - , t t I 1 f -r ( y ( r) (see the picture compute the integral: I I Jo cos \n I wwwv things you need to figure out is the limits of integration in I : . { , cji {f- : Lh ci rx ou(. ft n" -',,o \* i"L c{'.r : t"f j , , , I f . * l r - \ = * ! , \ _ L '-A lt* I .fi_ ?_ * ) { c r - t ; ? * z ) \ * u 5 d l t * t""',,. \*r :r -l t' "n a b , L], T" { \r () "1"t- i i f * ' * i'i\#i*foc,ile ; \w*,*J,r, t I * ...,"1*".r,.,* t irb {Vav"} I si,r{trL*L: PnosLpI\4 #I (30 PTs.) \nt.*f u q..;r""q ; 1*( {qa\r 1 ; : *.fl *"{" 4-.{" tf

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,cit tL"st) ) d t cl* n !e/,a i 'J{ = \:f. ( a. ost ) .{.,-,1* ts;^t) , (- Zs:^r _ ir/z : \*/t i l..-ti t*tt-s,,rb.ost + \hb.o,t { cic.:sit : (T/a 'l.iilr- {-ft,.rf cost 1 \6--st -(l Costsxtf } : 3/r. .. s't l!.!,;i, +as;^t fflri -.tizs..3s t #t pts.) Compute the line integral I tr. d,l of F over the-segmenf of the y-ocid'
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