Question

#10. Use spherical coordinates to evaluate to j** 122 de drody.

Answer 1

So E √4-x=yz 1272 dz dady -2.0. Now ocz<54-xr-ya Osv=14-42 . -2 <Y £2 Now z = √ 4-x%-y2 :> z=4-27 yr => x+yY+z=24 in spherical co-ordinate let nag sing coso,.. y = 8 sinf sino.... Z=8 cosa and artyrazr=gr=4 50, 82=2² => 3 = 2 & raries from oto 2 Now x=ra-yor > ar+y=4 → Sºsinno ( cosvot sinto) =4 => sin q = 1 => sin q=1 > q = 772

so, & varies from oto 7/2 and o varies from oto T. Therefore a ,2714-42 12 22 dzdx dy -20 roo 17, T 2.0 12 (89 cos? 0.59 sing de do do 2 72 T =121 s cos²o sing do do 1 (0) * sing as = 1202 jente sine * ) de - 12X32 7/2 32*12* i cosa sing dep. = I costop sina do Now I costa sing de let u= cosa => dle = - sing de 50 -1-u²de = - cos 34

Therefore - 3월 - g] - 38 151 + ] 384T 53. 지 = 804248