1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
PSYCHO15rus [73]
2 years ago
11

Evaluate the surface integral. S xz ds, s is the part of the plane 2x 2y z = 4 that lies in the first octant

Mathematics
1 answer:
maksim [4K]2 years ago
6 0

The value of the given surface integral is 4.

The given plane intercepts the coordinate axes at (2, 0, 0), (0, 2, 0), and (4, 0, 0). These point are the coordinates of a triangular region that we can parameterize using.

S(u,v)=(1-u)((1-u)(2,0,0)+u(0,2,0)+u(4,0,0)\\S(u,v)=(2(1-u)(1-v),2u(1-v),4v)

<h3>What is the surface integral?</h3>

A surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral. Given a surface, one may integrate a scalar field over the surface or a vector field.

with 0≤u≤1 and  0≤v≤1. Then the surface element ds  is equivalent to

ds=\||\:\left(s_u\times \:\:S_v\right)||dudv=12\left(1-v\right)dudv

The surface integral is then

\int \:\int \:_Sxzds=12\int _0^1\:\int _0^1\:\left(2\left(1-u\right)\left(1-v\right),2u\left(1-v\right),4v\right)dvdu=4

Therefore the value of the given surface integral is 4.

To learn more about the integral visit:

brainly.com/question/14295614

#SPJ2

You might be interested in
How do I solve this equation
netineya [11]
This should be correct I am sorry if it is not.
<span>-0.01511422733</span>
8 0
3 years ago
Read 2 more answers
Y-1=4y-2/3<br> y=_____<br> solve
Vikki [24]
Y - 1  =  4y - 2/3.      Move the ys over to one side,  +4y crosses over to become -4y,
                                  and -1 crosses over the right side to become +1.
y -4y  = -2/3  + 1
-3y  =    1 - 2/3
-3y =  1/3          Divide both sides by -3.

-3y/-3  = (1/3) / -3.
y  =  1/3  * -1/3
y =  - 1/9

7 0
3 years ago
Read 2 more answers
A recipe has a ratio of 2 cups of sugar to 6 cups of flour. How many cups of flour are used for each cup of sugar in the recipe?
statuscvo [17]
The ratio 2 to 6 can be reduced to 1 to 3. That means for every 3 cups of flour there is one cup of sugar. 
6 0
3 years ago
Read 2 more answers
Can i get some help on my test please?
Veseljchak [2.6K]

Answer:

Not proportional.

Step-by-step explanation:

The butterfly method multiples it like a butterfly. Ex. 5 times 3 is 15. 8 times 2 is  16. Therefore, not proportional.

5 0
3 years ago
Read 2 more answers
Create a tally chart with the data below
ladessa [460]
3 beach 2 skiing and 2 camp
5 0
3 years ago
Read 2 more answers
Other questions:
  • No receives a $5 discount each month on his cell phone bill because he signed up for autoplay from his bank account over the las
    12·1 answer
  • a scale on a map shows that 2 inches =25 miles part A how many inches on the map represents 60 miles part B how many miles are r
    8·2 answers
  • Central City High School's robotics team is at a competition. In the last round, the team earned 80 points for climbing over an
    14·1 answer
  • In an examination of purchasing patterns of shoppers, a sample of 36 shoppers revealed that they spent, on average, $50 per hour
    13·1 answer
  • Which of the points shown below are on the line given by the equation y = 2/3 x? Check all that apply. ​
    14·2 answers
  • NEED ASAP GIVING 20 POINTS.
    12·1 answer
  • The scientific notation of 0.004897
    11·1 answer
  • In 2.2, recall that on an open interval, the end points are not included in the interval. For example, the open interval (2, 4)
    6·1 answer
  • Differential equations <br> dy/dx = e^x-y
    9·1 answer
  • Which of the following problem types can always be solved using the law of cosines or sines? Check all that apply.A. SSSB. AAAC.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!