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
barxatty [35]
3 years ago
9

Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1)

and from (9, 1) to (10, 0)
Mathematics
1 answer:
viktelen [127]3 years ago
5 0
\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}

The first line segment can be parameterized by \mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle with 0\le t\le1. Denote this first segment by C_1. Then

\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt
=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt
=108

The second line segment (C_2) can be described by \mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle, again with 0\le t\le1. Then

\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt
=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt
=-\dfrac{229}3

Finally,

\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3
You might be interested in
What is $45.27 plus 16%?
Ghella [55]

Answer:

$52.51

Step-by-step explanation:

16% of 45.27 is 7.24

45.27 + 7.24 is $52.51

Hope this helps!

Stay safe!!

8 0
3 years ago
Read 2 more answers
Translate the expression: “the difference between twice a number and 23”
kherson [118]

Answer:

23- 2x

Step-by-step explanation:

Twice a number is 2 and "x" represents "a number"

Key words: Twice, Difference (subtraction)

7 0
2 years ago
The coefficients in the expression of (x+y)^4 are
DENIUS [597]

Answer:

the coefficients are 1,4,6,4,1.

Step-by-step explanation:

I hope this helps

4 0
3 years ago
Find f(-2) for f(x) = 3.2.<br> O A. 2/1<br> OB.<br> 36<br> O C. -36<br> OD. -12<br> 3/4
valina [46]

Answer:

3/4 (A)

Step-by-step explanation:

replace x with -2 in the function

3 · 2^-2  = 3 · 0.25

3 · 0.25 = 0.75

0.75 = 3/4

3 0
2 years ago
Read 2 more answers
Use the substitution method to solve the system of equation.choose the correct ordered pair. 2
Jlenok [28]
I’m not sure if the 2 is counted in the equation or not

Since x=4, substitute it for x in the other equation

4+3y=29
3y=25
Y=8.333333333

2(4)+3y=29
8+3y=29
3y=37
y=12.33333333
7 0
3 years ago
Other questions:
  • Mimi bought some fabric for a sewing project. The fabric cost $15.40 per meter. She bought 250 centimeters of fabric. How much d
    12·1 answer
  • Explain the different ways it it possible to add 2 rational numbers and get a negative number
    15·1 answer
  • Please help with this is important!
    7·1 answer
  • Each letter of the alphabet is written on a piece of paper and put in a hat. If a piece of paper is chosen at random, what is th
    13·2 answers
  • Need help...with this graph
    8·1 answer
  • In figure, what is the value of y?
    6·1 answer
  • I need help l don’t know what to do
    11·1 answer
  • Make y the subject of the following equation.
    10·2 answers
  • Translate the sentence to an algebraic expression r minus 7
    13·1 answer
  • Which correctly describes how the graph of the inequality by 6y - 3x &gt; 9 is shaded?
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!