20EFinalSolns!!!

20EFinalSolns!!! - 1. (6 points) Evaluate 1 1 11 sin (x 3 )...

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Unformatted text preview: 1. (6 points) Evaluate 1 1 11 sin (x 3 ) dxdy. y=o x=..fji by changing the order of integration. (Note: you need not simplify trigonometric expressions in your final answer.) , I I ' I XL , t SV'""'i Sinlx:'')dxd\ -:: So So S\l'Ilx.~) c1~dx: j ~ i CJ 2 Y-"'IV) ~ ~ :-f) .c--J.-2) if J' \J, (j) s~ >l &X ~ ~ I J ~cJ ~ ""5 -- Q ~ ~~,~ ~:t E fi ~ .>< 57 ~ j Q- e ~ ~ --Q <:J $ =~J~H l x~-r S~x3, I 0 d x \ vt=x'3 Xl cs ir) ",3 d;>< d~ = 3,,2dx ~: X =0 -=t 4 ::.6 l X -=., =::, \A :::.. J -- J() r ~ Vrtu d~ _\ "3 LDS u. \ 1 - \ ,-- eD~ \ ~- Cos () 3 3 -\ 3 (oS, \- l. 3 2. (6 points) Find an appropriate change of variables to evaluate J In (x + y) eZ'-i' dxdy, where R is the square with vertices (2,0), (0,2), (-2,0), (0, -2). (Hint: first determine equations for each side of the square R.) /'1-- v :' ',. ~ ~ ~ ~-:; u+--- v --2<\1..<"''- "" = X Jr "-'\ 2- \j -= 'X- 'j ~ LA-V-L,zV<'2 ~:= 1- I J )(/d~ dx/dv \/2 til.' _ t \ -= - \ t:t-~ 2.. 1 d~/dv. ~~" \/2. -:"2 Sf ~2 '12 d R. Lx \-~l e Xd~ -= 5S u e U-v (-i~ 'd V d LA -::. 121~ \Ae ~" ci" d'" -:: 12 \) ~elA~ \:2- cl~ -') lA -2-2 -2- 2. \.4 -24 \ 1-- '2,-,\ _ ~'2. 2u e __ E:,-- e -e du --2 . 2--2- '?I..\ 2,,\ \ 1- _ s- \-e -- e2~\: -= le.Lt y _- ~ - 2--2 I'r -, /~ '), I'- 'Ix ~ &~,~ -r+~_ '< 1--2.....
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20EFinalSolns!!! - 1. (6 points) Evaluate 1 1 11 sin (x 3 )...

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