Question

Question 11 (Extra Credit Questions) (20 points) 6 1) Use the spherical coordinates to evaluate the triple integral $15 (32 +y*+22312° dV; where E is the region between the spheres of radius 2 and 3 centered at the origin. (10 points) c0 CP 2) Use Green's theorem Pdx + Qdy = Ox HA @y ER STUDENT. WON a е о Type here to search

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Answer 1

solution I = dv Let SIA 6 (x*+ y2 +22) 3/2 To convert it into spherical co-ordinates Put x=rsin & cos o y=rsin & sino 3 x² + y² + z² = 912 Z = MCOS • dv = r² sind der dodo Here, E is the region between the sphere 2 and 3 centered at origin. 50, 2sris 3 O sor in first octant for 8 octants, multiply by 8. of radius Eld 2 T/2 1/2 6 x er² sind der dodo so I = 8 3 r 0=0 $20 Mz2 ST 4072 IT/ 3 T/ do der = 48 sind do r $=0 r=2 TT/ 3 en = 48 [0]" E COS • 97 2 - 48 (5-0) [(0-1]• (en 3-dn 2) - 24 T en 2