Evaluate the surface integral. s x2 + y2 + z2 ds s is the part of the cylinder x2 + y2 = 25 that lies between the planes z = 0 and z = 4, together with its top and bottom disks

Over the cylinder's lateral face: parameterize this part of (call it ) by

with and , then the surface element is

Over the bottom disk: parameterize this part () by

with and , then

(this will be the same for the top disk) and the integral is

Over the top disk (): the only change is replacing with , so that the integral is

Then the total surface integral is the sum of the partial surface integrals:

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step-by-step explanation:

1+2+3+4+5+6+7+8+9+10 = 55

2*10 = 20

55-20 = 35

24

step-by-step explanation:

if it takes 8 pounds to make 12 divide 12 by 8 and you get 1.5, 1.5 x 16 = 24