Question

Evaluate \iint_S \text{CurlF} \cdot \text{n}dS ... F(x,y,z) = -yzi + 0j + xyk, and S: z = 2\sqrt{x^2 + y^2} between the lines y = 2 and y = 4, and n is upward. a. 32\pi b. 16\pi c. 48\pi d. 28\pi e. 24\pi

          Evaluate \iint_S \text{CurlF} \cdot \text{n}dS ...
F(x,y,z) = -yzi + 0j + xyk, and
S: z = 2\sqrt{x^2 + y^2} between the lines y = 2 and y = 4, and n is upward.
a. 32\pi
b. 16\pi
c. 48\pi
d. 28\pi
e. 24\pi

Evaluate CurlF ·ndS ...
F(x,y,z) = -yzi + 0j + xyk, and
S: z = 2√(x^2 + y^2) between the lines y = 2 and y = 4, and n is upward.
a. 32πb. 16πc. 48πd. 28πe. 24π

Added by Jonathan C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/22/2023

Step 1

Step 1: Calculate the curl of F The curl of F is given by: CurlF = ∇ x F = (∂(xy)/∂z - ∂(0)/∂y)i - (∂(-yz)/∂z - ∂(xy)/∂x)j + (∂(-yz)/∂y - ∂(0)/∂x)k = (0 - 0)i - (0 - 0)j + (-z - 0)k = -zk Show more…

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Evaluate ∬_(S) CurlF * ndSdots F(x, y, z) = -yz i + 0 j + xy k, and S: z = 2√(x^(2) + y^(2)) between the lines y = 2 and y = 4, and n is upward. a. 32π b. 16π c. 48π d. 28π e. 24π Urgent ASAP Evaluate ∬∬_(S) CurlF * nds F(x, y, z) = -yz i + 0 j + xy k, and S: z = 22 + y between the lines y = 2 and y = 4, and n is upward. a. 32π b. 16π c. 48π d. 28π e. 24π