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

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.

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step-by-step explanation: