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
poizon [28]
3 years ago
6

Evaluate the line integral, where C is the given curve. C (x + yz) dx + 2x dy + xyz dz, C consists of line segments (1, 0, 1) to

(2, 4, 1) and from (2, 4, 1) to (2, 6, 4)
Mathematics
1 answer:
Bess [88]3 years ago
5 0

Parameterize the first line segment C_1 by

\vec r(t)=(1,0,1)(1-t)+(2,4,1)t=(1+t,4t,1)

and the second line segment C_2 by

\vec s(t)=(2,4,1)(1-t)+(2,6,4)t=(2,4+2t,1+3t)

both with 0\le t\le1. Then

\displaystyle\int_{C_1}(x+yz)\,\mathrm dx+2x\,\mathrm dy+xyz\,\mathrm dz

\displaystyle=\int_0^1\bigg((1+5t)\cdot1+2(1+t)\cdot4+(1-t)4t\cdot0\bigg)\,\mathrm dt

=\displaystyle\int_0^1(9+13t)\,\mathrm dt=\frac{31}2

and

\displaystyle\int_{C_2}(x+yz)\,\mathrm dx+2x\,\mathrm dy+xyz\,\mathrm dz

\displaystyle=\int_0^1\bigg((2+(4+2t)(1+3t))\cdot0+2(2)\cdot2+2(4+2t)(1+3t)\cdot3\bigg)\,\mathrm dt

\displaystyle=\int_0^1(32+84t+36t^2)\,\mathrm dt=86

Then

\displaystyle\int_C(x+yz)\,\mathrm dx+2x\,\mathrm dy+xyz\,\mathrm dz=\frac{31}2+86=\boxed{\frac{203}2}

You might be interested in
Which part of an atom is actively exchanged or shared in a chemical bond? proton neutron electron all of the above
Olegator [25]
The answer is the proton
5 0
3 years ago
Read 2 more answers
Find the value of 7!?
Schach [20]
The question isn’t clear, post the question so I could help :) !
5 0
3 years ago
Read 2 more answers
A composite figure is made up of two or more
Marizza181 [45]
it is made up of figures
7 0
3 years ago
Which terms complete the factorization of x2 27x 162 represented by the model? 27, 9x, 18x 9, 9x, 18x 27, 9x, 27x 9, 9x, 27x
olga nikolaevna [1]

Answer: 9, 9x, 18x

Step-by-step explanation:

Hope it helps :D

3 0
2 years ago
Brainliest for correct answer
polet [3.4K]

Answer:

Step-by-step explanation:

its too small. i cant read it

7 0
3 years ago
Other questions:
  • What is the inverse of the function f(x)= 1/4x - 12?
    13·1 answer
  • Calculate the length of the unknown side of this right angled triangle
    6·1 answer
  • Which pair of numbers are not opposites?
    15·2 answers
  • Mary is playing basketball. She scored 11 baskets in 15 free throws.What is the experimental probability that she will NOT score
    14·1 answer
  • Identify the equation that means eleven less than x is twenty-three
    15·1 answer
  • 1. What statement describes the relationship between the graph of the equation y = −|x| and the graph of the equation y = −|x| −
    10·1 answer
  • Name the minor arc and find its measure.
    9·1 answer
  • What is the volume of the cone?
    14·1 answer
  • 3/4(-10+2/5) Please help I will mark branliest​
    5·2 answers
  • Solve for x: 9x-1=10x+9<br><br> How do you get x off one side and onto the other, please explain
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!