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
trasher [3.6K]
3 years ago
14

Consider f and c below. f(x, y) = x2 i + y2 j c is the arc of the parabola y = 2x2 from (−1, 2) to (1, 2) (a) find a function f

such that f = ∇f. f(x, y) = x3 3​+ y3 3​ correct: your answer is correct. (b) use part (a) to evaluate c ∇f · dr along the given curve
c.
Mathematics
1 answer:
Korvikt [17]3 years ago
5 0
If there is some scalar function f(x,y) such that

\nabla f(x,y)=\mathbf f(x,y)=x^2\,\mathbf i+y^2\,\mathbf j

then we want to find f such that

\dfrac{\partial f}{\partial x}=x^2\implies f(x,y)=\dfrac{x^3}3+g(y)
\dfrac{\partial f}{\partial y}=y^2=\dfrac{\mathrm dg}{\mathrm dy}\implies g(y)=\dfrac{y^3}3+C
\implies f(x,y)=\dfrac{x^3}3+\dfrac{y^3}3+C

So the vector field \mathbf f(x,y) is conservative, which means the fundamental theorem applies; the line integral of \mathbf f along any path \mathcal C parameterized by some vector-valued function \mathbf r(t) over a\le t\le b is given by

\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=\int_{t=a}^{t=b}\mathbf f(\mathbf r(t))\cdot\dfrac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt=f(\mathbf r(b))-f(\mathbf r(a))

In this case,

\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f(1,2)-f(-1,2)=\dfrac23
You might be interested in
A scuba diver was swiming at an elevation of -8 meters. A shark was swimming at an elevation of -29 meters. Find the diffrence b
KonstantinChe [14]

Answer:

21

Step-by-step explanation:


4 0
2 years ago
Read 2 more answers
There are 84 new houses being built in a neighborhood. Last month, 1/3 of them were sold. This month, 5/7 of the remaining house
noname [10]
There are a total of 16 houses left
4 0
2 years ago
4-7x=1-6x <br><br> Please explain why the answer is the answer and I’ll give brainlist
Mrac [35]

Answer:

3

Step-by-step explanation:

5 0
2 years ago
Evaluate a + b for a = 2 and b = 3
Vikki [24]

Answer:

5

Step-by-step explanation:

2+3+5

5 0
3 years ago
Find 90% of $800 [1]
laiz [17]

Answer:

$720.00

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • What expression is equivalent to 7-2z-4(z^3-z^3+4z^2+11z+14/z+2)
    11·2 answers
  • A price p (in dollars) and demand x for a product are related by
    12·1 answer
  • there are 165 different plants in the school garden.of these ,132 will flower in spring.what percent of the plants will flower i
    15·1 answer
  • The penguin nursery is open two times a day: 2/3 hour at noon and 5/12 hour in the afternoon. How much time is the penguin nurse
    9·2 answers
  • Joe is arranging video games on shelves. He has 48 playstation games and 36 xbox games, Each shelf will have the same number of
    5·1 answer
  • Emily ha 6 pounds of grapes. She splits the grapes into smaller 1/3 pound bunches. How many bunches of grapes can she make ?
    13·1 answer
  • 4&lt;-2x+3&lt;9 <br> Solve the inequality
    5·2 answers
  • GIVING BRAINLIEST FOR BEST ANSWER!
    9·2 answers
  • Find the measure <br>someone please help ​
    12·1 answer
  • Mrs. Lola and Mr. John bought tacos and burgers for lunch 2 days in a row. One day they bought 4 burgers and 3 tacos for $269, t
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!