C Determine If The Vector x M Mathematics Michigan x y D WegWork mth 234 fs x C
ID: 2878028 • Letter: C
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C Determine If The Vector x M Mathematics Michigan x y D WegWork mth 234 fs x C https://ww 4.mat msu ed /webwork 2/mth 234 fs16 73000/Hw33 16.7- Surface Integrals/1/?user-grego191&key; 112e28974ac999591b73foed3d5555&effectiveUser; greg Problem Previous Problem List Next User Settings Grades (1 point) Evaluate the surface integra -3ayz ds Problems Where S1 is the cone with parametric equations a w cos(v), y u sin(v), 2- Problem 1 Problem 2 and 0 4, 0 Problem 3 Problem 4 du dud Problem 5 Problem 6 where Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Eval ate Note: You can eam partial credit on this problem. 5:40 PM 9 Ask me anything 2/2/2016Explanation / Answer
given x =ucos(v) , y=usin(v),z =u
r(u,v)=<ucos(v) , usin(v),u>
ru=<cos(v) , sin(v),1>
rv=<-usin(v) , ucos(v),0>
ruxrv=<(sinv*0)-(ucosv*1),(-usinv*1)-(cosv*0),(cosv*ucosv)-(-usinv*sinv)>
ruxrv=<-ucosv,-usinv,u>
|ruxrv|=[(-ucosv)2+(-usinv)2+u2]
|ruxrv|=[u2+u2]
|ruxrv|=u2
u1=0,u2=4,v1=0,v2=3/2
S -3xyz dS
=[0 to 3/2][0 to 4] -3(ucos(v)* usin(v) *u) u2 du dv
=[0 to 3/2][0 to 4] -32 u4cos(v)sin(v) du dv
=[0 to 3/2][0 to 4] (-32/5) u5cos(v)sin(v) dv
=[0 to 3/2](-32/5)(45-05)cos(v)sin(v) dv
=[0 to 3/2](-30722/5)cos(v)sin(v) dv
=[0 to 3/2](-30722/5)(1/2)sin2(v)
=[0 to 3/2](-15362/5)sin2(v)
=(-15362/5)[sin2(3/2) -sin2(0)]
=(-15362/5)[ 1-0]
=(-15362/5)
S -3xyz dS=(-15362/5) -434.446
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