Evaluate the surface integral of f over the surface S. S is the hemisphere x2 + y2 + z2 = 7, z ≥ 0; f(x, y,z) = z2 Question 2 options: A) 196π B) π C) π CHEGG

The question is not correct.

The correct question is sphere x2 +y2 + z2 = 36, f(x,y,z) = x2+y2  for z ≥ 0

Step-by-step explanation:

The given function is where S is the hemisphere, .

To evaluate the surface integral

Now using the polar coordinates, we get

x = r cos θ, y = r sin θ for 0 ≤ θ ≤ 2π and x² + y² = r²

Now given

x²+y²+z=36   ......(i)

Put z = 0 in equation (i), we get

⇒ r² = 36, r = 6

Now writing the limits,

0 ≤ r ≤ 6,  0 ≤ θ ≤ 2π and f(x,y,z) = x²+y²=r²

Hence, surface integral

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