A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 one year ago
Evaluate the line integral 3x ds, where C is the quartercircle x^2+y^2=4 from (2, 0) to (0, 2).
 one year ago
Evaluate the line integral 3x ds, where C is the quartercircle x^2+y^2=4 from (2, 0) to (0, 2).

This Question is Closed

SithsAndGiggles
 one year ago
Best ResponseYou've already chosen the best response.1Parameterize \(C\) by \(x(t)=2\cos t,\;y(t)=2\sin t, \text{ with }0\le t\le\frac{\pi}{2}.\) I'm not sure what the "ds" means, though. Is that supposed to mean \(\sqrt{1+\left(\frac{dy}{dt}\right)^2}\), or something like that?

SithsAndGiggles
 one year ago
Best ResponseYou've already chosen the best response.1Are you absolutely sure? Because it could also be \(\frac{dx}{dt}, \text{ or }\frac{dy}{dx}.\)

SithsAndGiggles
 one year ago
Best ResponseYou've already chosen the best response.1^^ instead of \(\frac{dy}{dt},\) I mean.

Idealist
 one year ago
Best ResponseYou've already chosen the best response.0But where did you get the x(t)=2/sin(t) and y(t)=2/cos(t)?

SithsAndGiggles
 one year ago
Best ResponseYou've already chosen the best response.1Those are the parametric equations of a circle with radius 2 (centered about the origin). They describe the path C.

Idealist
 one year ago
Best ResponseYou've already chosen the best response.0What's the next step I should do?

SithsAndGiggles
 one year ago
Best ResponseYou've already chosen the best response.1Set up your integral. Depending on what dS is supposed to be, I'm pretty sure it'd be \[\large\int_C3x\;dS=\int_0^{\frac{\pi}{2}}3\cos t\sqrt{\cdots}\;dt\]

Idealist
 one year ago
Best ResponseYou've already chosen the best response.0But how to find the ds?

SithsAndGiggles
 one year ago
Best ResponseYou've already chosen the best response.1Ah, according to this link (http://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsPtI.aspx), \[dS=\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}\;dt\] In my earlier posts, I was stuck in an arclengthmindset. So, the integral is \[\large\int_0^{\frac{\pi}{2}}3\cos t\sqrt{\left(2\sin t\right)^2+\left(2\cos t\right)^2}\;dt\]
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.