Question

8. Let $f(x, y, z) = \sqrt{x^2 + y^2 + z^2}$, evaluate the following surface integrals: (a) $\iint_S f(x, y, z)dS$, where $S: z = \sqrt{x^2 + y^2}, x^2 + y^2 \le 4$. (**) (b) $\iint_S f(x, y, z)dS$, where $S: z = \sqrt{x^2 + y^2}, (x - 1)^2 + y^2 \le 1$ 9 Let $f(x, y, z) = x^2 + y^2 + z^2$ evaluate the following surface integrals

          8. Let $f(x, y, z) = \sqrt{x^2 + y^2 + z^2}$, evaluate the following surface integrals:
(a) $\iint_S f(x, y, z)dS$, where $S: z = \sqrt{x^2 + y^2}, x^2 + y^2 \le 4$. (**)
(b) $\iint_S f(x, y, z)dS$, where $S: z = \sqrt{x^2 + y^2}, (x - 1)^2 + y^2 \le 1$
9 Let $f(x, y, z) = x^2 + y^2 + z^2$ evaluate the following surface integrals

8. Let f(x, y, z) = √(x^2 + y^2 + z^2), evaluate the following surface integrals:
(a) f(x, y, z)dS, where S: z = √(x^2 + y^2), x^2 + y^2 ≤ 4. (**)
(b) f(x, y, z)dS, where S: z = √(x^2 + y^2), (x - 1)^2 + y^2 ≤ 1
9 Let f(x, y, z) = x^2 + y^2 + z^2 evaluate the following surface integrals

Added by Dustin R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vikash Ranjan

Step 1

The surface S is a circular disk centered at the origin with radius 2. We can parameterize the surface using cylindrical coordinates as follows: x = r cos(theta) y = r sin(theta) z = r^2 The unit normal vector n can be found by taking the partial derivatives of Show more…

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8. Let f(x, y, z) = 2 + y^2 + z^2, evaluate the following surface integrals: (a) âˆ¬f(x,y,z) dS, where S: z = x^2 + y^2, x^2 + y^2 â‰¤ 4. (**) (b) âˆ¬(x,y,z) dS, where S: z = x^2 + y^2, (x - 1)^2 + y^2 â‰¤ 1