Question

4. For each of the following, compute the integral or show it doesn't exist: 2 1 (a) SR3 dV R3 1+x2 + y2 +22 (b) Sc (22+42 2dA where C = {(x,y) : x2 + y2 < 1} (c) Ss zvydA where S dA where S = {(x, y):1 < x,0 <y <} 1 9 9

Answer 1

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/ x2 dA where C = {(x, y): x²+4²<1} (x²74272 Putting dA=rdrdo x=rcoso, y=r8tho x²+ y = r2 ie Into polar form and limits of R o to 1 x²742</ ral and o from 0 to 20 e²costo edrdo (92) 2 jos 2M 1 0 ra I costo drdo o

-Parndo s't do st gen lacoso do L dr 2 20 oft of anal! 247 Los20 do 20. = T & Ini-dno Does not exist as Ino does not exist

o) IdA where s=f(x,y): 15x,osyst? xrý S Region of Integration The shaded region & the area (region) of Integration Sevda - g z t dy dre x=1 y=0 y=h o X=1 post 2ykajte de - 5744344 1 Sx dx = x hoti htl jot da Xh -3/2 da -1/2 2x -1/2 2-4 -4 -4(5 - 7) = - 410-1) dA S