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
dedylja [7]
3 years ago
6

Use Green's Theorem to evaluate F · dr. C (Check the orientation of the curve before applying the theorem.) F(x, y) = e−x + y2,

e−y + x2 , C consists of the arc of the curve y = cos(x) from − π 2 , 0 to π 2 , 0 and the line segment from π 2 , 0 to − π 2 , 0
Mathematics
1 answer:
Yuki888 [10]3 years ago
3 0

Notice that C is traversed clockwise. Green's theorem applies to curves with a counterclockwise orientation, so we'll have to multiply the area integral by -1.

By Green's theorem, with the vector field \vec F(x,y)=P(x,y)\,\vec\imath+Q(x,y)\,\vec\jmath,

\displaystyle\int_C\vec F\cdot\mathrm d\vec r=-\iint_D\left(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}\right)\,\mathrm dA

where D is the region with boundary C. The partial derivatives are

\dfrac{\partial(e^{-y}+x^2)}{\partial x}=2x

\dfrac{\partial(e^{-x}+y^2)}{\partial y}=2y

so that the double integral is

\displaystyle\iint_D\left(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}\right)\,\mathrm dA=\int_{-\pi/2}^{\pi/2}\int_0^{\cos x}2(y-x)\,\mathrm dy\,\mathrm dx=\boxed{\frac\pi2}

You might be interested in
The graph of g(x) = (1/2)x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)?
larisa [96]
Reflect across y axis means that you replace x with -x

f(-x)=2(-x)=-2x
g(x)=-2x
de graph is the one that passes through (0,0) and (1,-2) and -1,2)
4 0
3 years ago
Read 2 more answers
Two competing sports equipment suppliers sell footballs at different prices. Supplier A charges $85 in shipping, and charges $2.
S_A_V [24]
Supplier A: $188.6
Supplier B: $221.6

I hope I helped but I honestly have no idea if I did. Anyway sorry if I didn't. Good luck.
7 0
3 years ago
What is the answer to 3k=−2(7+2k)
laiz [17]
I think k equals negative 2, or -2.<span>
</span>
7 0
4 years ago
Read 2 more answers
How does an expression differ from an equation?
rewona [7]
An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.
8 0
3 years ago
Please answer me quickly first one to answer will get Brainlyest
Debora [2.8K]
D and a is the answer
8 0
3 years ago
Other questions:
  • Solve the equation without the use of a calculator. please Help!!! Thank you!!!<br> 5=2x^2+3
    10·1 answer
  • Question in screenshot.
    8·1 answer
  • GET BRAINLIEST ANSWER FIRST
    9·2 answers
  • I NEED HELP ASAP I DONT UNDERSTAND THIS!!
    8·1 answer
  • 1. Find the slope given the points (-6,7) and (1,8)<br> -1/7<br> 1/7<br> -7/1<br> 7
    5·1 answer
  • Which is an equation of the line with slope –3 and passes through (2, –1)
    14·1 answer
  • Find the slope of the line through the pair of points.
    12·2 answers
  • What decimal is equivalent to 15%
    9·2 answers
  • E. What is the median temperature for the data shown in the table?
    11·1 answer
  • The highway mileage (mpg) for a sample of 8 different models of a car company can be found below. Find the mean, median, mode, a
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!