for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x,y,z)=xi+2yj+3zk

S is the cube with vertices

Reeves
2020-11-03
Answered

Evaluate the surface integral

${\int}_{S}F\cdot dS$

for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x,y,z)=xi+2yj+3zk

S is the cube with vertices$(\pm 1,\pm 1,\pm 1)$

for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x,y,z)=xi+2yj+3zk

S is the cube with vertices

You can still ask an expert for help

unessodopunsep

Answered 2020-11-04
Author has **105** answers

Remember that

Let's start with the top side of the cube. Along that face, the outward normal points up. I.e.

Also along the top face we have

=3(2)(2)=12 Along the left face (pretend you're sitting somewhat out on the positive

At this point hopefully you get the idea so I'm just going to quickly list the rest of the integrals and their values:

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Evaluate the line integral, where C is the given curve

C xy ds

C:$x={t}^{2},y=2t,0\le t\le 5$

C xy ds

C:

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Evaluate the following integrals.

$\int ({\mathrm{csc}}^{2}x+{\mathrm{csc}}^{4}x)dx$

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Find the integral: $\int \frac{1}{\sqrt{2{t}^{2}-6t+1}}dt$.

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To find:

The value of$\underset{x\to 0}{lim}\left(\frac{{4}^{3x}-{4}^{x}}{{4}^{x}-1}\right)$ if it exists. If limit does not exist , then find out if one-sided limit exists.

The value of

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Suppose that

asked 2021-08-19

A curve is given by the following parametric equations. $x=20\mathrm{cos}t,y=10\mathrm{sin}t$ .

The parametric equations are used to represent the location of a car going around the racetrack.

a) What is the cartesian equation that represents the race track the car is traveling on?

b) What parametric equations would we use to make the car go 3 times faster on the same track?

c) What parametric equations would we use to make the car go half as fast on the same track?

The parametric equations are used to represent the location of a car going around the racetrack.

a) What is the cartesian equation that represents the race track the car is traveling on?

b) What parametric equations would we use to make the car go 3 times faster on the same track?

c) What parametric equations would we use to make the car go half as fast on the same track?