Question: Let (mathcal{S}) be the disk (x^{2}+y^{2} leq 1) in the (x y)-plane oriented with normal in the positive (z)-direction. Determine (iint_{mathcal{S}} mathbf{F} cdot d mathbf{S})

Let $\mathcal{S}$ be the disk $x^{2}+y^{2} \leq 1$ in the $x y$-plane oriented with normal in the positive $z$-direction. Determine $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$ for each of the following vector constant fields:
(a) $\mathbf{F}=\langle 1,0,0angle$
(b) $\mathbf{F}=\langle 0,0,1angle$
(c) $\mathbf{F}=\langle 1,1,1angle$

Step by Step Solution

★★★★★

3.35 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The unit normal vector to the oriented disk is mathbfnlan... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Calculus 4th Questions!

Members AB and BC can each support a maximum compressive force of 800 lb, and members AD, DC, and BD can support a maximum tensile force of 1500 lb. If a = 10, determine the greatest load P the truss...

Illustrate with example why one type of RAM is considered to be analog and the other digital. Justify the difference between a simple CAV system and a multiple zone recording system.

Prvoide detail explanation Which project will you realize? Net Present Value Calculation You manage a small company producing plastic pallets. Your (business) customers are companies using plastics...

Let $\mathbf{F}=\langle z, 0, yangle$, and let $\mathcal{S}$ be the oriented surface parametrized by $\Phi(u, v)=\left(u^{2}-v, u, v^{2}ight)$ for $0 \leq u \leq 2$, $-1 \leq v \leq 4$....

Use the Divergence Theorem to evaluate the flux $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$. $\mathbf{F}(x, y, z)=\left\langle x y^{2}, y z^{2}, z x^{2}ightangle, \mathcal{S}$ is the...

Use the Divergence Theorem to evaluate the flux $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$. $\mathbf{F}(x, y, z)=\left\langle x^{2} z, y x, x y zightangle, \mathcal{S}$ is the boundary...

Use the Divergence Theorem to evaluate the flux $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$. \(\mathbf{F}(x, y, z)=\left\langle e^{z^{2}}, 2 y+\sin \left(x^{2} zight), 4 z+\sqrt{x^{2}+9...

Compute $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$ for the given oriented surface. $\mathbf{F}=\langle y, z, xangle$, plane $3 x-4 y+z=1$, $0 \leq x \leq 1,0 \leq y \leq 1$,...

Use the Divergence Theorem to evaluate the flux $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$. $\mathbf{F}(x, y, z)=\left\langle e^{x+y}, e^{x+z}, e^{x+y}ightangle, \mathcal{S}$ is the...

Use the Divergence Theorem to calculate $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$ for the given vector field and surface. \(\mathbf{F}(x, y, z)=\left\langle\sin (y z), \sqrt{x^{2}+z^{4}},...

On 1 November 1992 Mary had a nice home in Sydney and also acquired a second-hand yacht for $88337. Mary borrowed $82,000 of the money from XYZ Bank to buy the yacht.. The loan was a fixed interest...

Water flows through a 180 reducing bend, and the bend is in the vertical plane. The discharge rate is 0.25 m/s, and the pressure at the centre of inlet section is 150 kPa gauge. If the bend volume is...

Weiland, Inc., has 3 5 0 , 0 0 0 shares outstanding that sell for $ 8 5 per share. The company plans a 2 - for - 1 stock split. How many shares will be outstanding after the split? Multiple Choice 8...

How is your DMO capturing visitor metrics such as arrivals, length of stay, spend, and repeat visitation? What limitations can you identify in the data collection?

Use the result of Exercise 5.5.83 to compute the average volume of inhaled air in the lungs in one respiratory cycle.

Use the diagram to show that if f is concave upward on [a, b], then +b fon >. a+b 2

Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = tan x, y = x, x = /3; about the y-axis

In January 2022, the management of Kinzie Company concludes that it has sufficient cash to permit some short-term investments in debt and equity securities. During the year, the following...

Firm pays a current dividend of $1.00 Growth rate is 20% for next two years Growth then declines over 6 years to a stable rate of 5% Required return is 10% Current stock price is $50 Assumes three...

Chapter 7 Sage Aircare services answers- journal entries, trail balance, balance sheet