2 !x x dy 0 00 lo o ex. by transforming to a triple integral evaluate i= jjxdydz + x°ydzdx + x°z dx dy where sis the closed surface bounded by the planes z = 0,

2 !x x dy 0 00 LO o Ex. By transforming to a triple integral evaluate I= JJxdydz + x°ydzdx + x°z dx dy where Sis the closed surface bounded by the planes z = 0, z = b and the cylinder x + y2 = a2 By divergence theorem, the required surface integral| is equal to the volume integral. a? Sol. >y 3x +x +x*) dxdydz z-0 y--a x-a-y2) - 4x5 a -x dxdydz y=0 Jo x Va- 20 3 dlydz- 3 Jz=0Jy=0 -v) dydz 3/2 Jx=0 3-=yb-vy"ay y=0 Put y = a sin t so that dy = a cos t dt = ba' cos' t(acost) dt =a'bcos' tdt a'b =ra'b 4.2 2 4 3 3 Contact Us: Website: www.eduncle.com Email: support@eduncle.com Call Us: 7665435300 28