Asked Jul 26, 2019

Use the Divergence Theorem to compute the net outward flux of the field

F=<x,2y,-z> across the surface​ S, where S is the boundary of the tetrahedron in the first octant formed by the plane x+y+z=2

Expert Answer

Step 1

From the Divergence theorem, for a positively oriented boundary surface (outward Normal) of region E the flux is equal to triple integral of divF over the region E.

Step 2

Find the range of x,y and z as follows. Also observe that the plane is on the first quadrant.


Image Transcriptionclose

The range of z varies from value of Z= 0 to value of z on plane z 2 - x-y which implies 0sz2-xy The range of y varies from value of y =0 to value of z on plane y 2-x which implies 0s ys2-x The range ofx varies from value of x = 0 to value ofz on plane x = 2 which implies 0Sxs2

Step 3

The divF can be calculated as fo...


Image Transcriptionclose

divF = div((x,2y,-z)) (2y)+(-z) ôz =1+2-1 = 2


Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in




Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A

Q: Evaluate the following integrals (a) x^5dx (b)(5^2+x^10)dx (c) (12x^5+12x^3-7)dx (d) (x^3-7-(3/x^4))...

A: You have asked a question with multiple sub parts. I will address the first three of them. Please po...


Q: How can I get the result? Which is the result?

A: In a graph, a function is said to be increasing if it is rising from left to right and is said to be...


Q: What is the position at time t of a car that is accelerating at a rate of 5 meters per second square...

A: To determine the position of the car from the given data. (note that s =20 when t=2, not as given)


Q: Please help

A: Since f(x0,y0) is minimum of f(x,y). Then g(0) is minimum of g(t). That means g(0)&lt;g(t) for t any...


Q: Need help solving the equation that is attached

A: x-&gt;4^+ means x is slightly greater than 4. That means we have to use the part when x&gt;4 to find...


Q: Maximize f(x, y, z) = 2x + 7y +9z on the sphere x + y+z = 67. Additional Materials eBook

A: f(x,y,z) = 2x + 7y + 9z and g(x,y,z) = x2 + y2 + z2 Approach:We will make use of the method of Lagra...


Q: For  y= (x^4/4)-(x^3/3)-2   (a) Find y' =f'(x). (b) Find the critical values. (c) Find the critical ...

A: We are given a function  


Q: please show ALL your steps

A: we are given a function 


Q: Optimization Problem A rectangle is constructed with its base on the diameter of a semicircle with r...

A: a)Let x and y be the base and height of the rectangle, respectively.Given that, the rectangle is con...