Consider the following integral. (/ (x2 + y2) dv, where E lies between the spheres x" + y- + 2" = 1 and x2 + y2 + 2 = 4 Write an equivalent integral using spherical coordinates. dp de do A = B = Evaluate the integral.Answere : Given that IS (x24 2 ) du. Wheree E lies between the graph - 2742+2?= 1 and x2+ 72+ 2 2 = 4 . Lot 2 : psinp loso y = psinp sino z =p losQ . J = 0 (x82) Ox on 3 ( p, 0, 9 ) DO 04 RQ = - p sinc . :. 1JI = p-sin Q . 02 02 02 ispsg. 7 . 2X pasin't . p-sing. p . do. dop. 4= 0 0= 0 P= s 21 = - 1 . do. ( . py sinap dp. d. $20 020 p 21 = 27 1 2 sin . 24. 4=0 2 27. 32 - 1 ) . sin p. d4 . 7/2 627 sinsp.d Q. = 625. 2 sing. d4 . 5 428 420 = 62 5 .15 1 (3+1 ) use " Gamma function . 5 17 (3+ 2) 62 73/2 1 ( 2 ) 62 3/2 1 . 17 ( 572 ) = 3/2 17 ( 3/2) 5 1 ( 5/2 ) 5 62 x 4 5 3 = 51 .9409 2 51. 941 A = B = 2