A community for students.
Here's the question you clicked on:
 0 viewing
meggiesmermaid
 2 years ago
Evaluate the line integral
(x2+y2)dx+2xydy
where is the path of the semicircular arc of the circle x2+y2=64 starting at (8,0) and ending at (−8,0) going counterclockwise.
meggiesmermaid
 2 years ago
Evaluate the line integral (x2+y2)dx+2xydy where is the path of the semicircular arc of the circle x2+y2=64 starting at (8,0) and ending at (−8,0) going counterclockwise.

This Question is Closed

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1did you want to check an answer, or are you stuck?

meggiesmermaid
 2 years ago
Best ResponseYou've already chosen the best response.0\[512\int\limits_{0}^{\pi} \cos^2t sint  \sin^3t\] im stuck at how to integrate this.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1use\[u=\cos t\]and\[\sin^2t=1\cos^2t\]

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1how did you get cos^2t*sint for x^2+y^2dx ?

meggiesmermaid
 2 years ago
Best ResponseYou've already chosen the best response.0i keep getting confused but heres where i started \[\int\limits_{0}^{\pi} ((8cost)^2 + (8sint)^2)(8sint) + 2(8cost)(8sint)(8cost)dt\]

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1yes, and that can be written\[\int_0^\pi512(\sin^2t+\cos^2t)(\sin t)dt+\int_0^\pi512(2\cos^2t\sin t) dt\]

meggiesmermaid
 2 years ago
Best ResponseYou've already chosen the best response.0\[512\int\limits_{0}^{?\pi} sint dt +1024\int\limits_{0}^{\pi} \cos^2tsint\] which becomes this

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1yes, which you can recombine to form this\[512\int_0^\pi2\cos^2t\sin t\sin tdt\]

meggiesmermaid
 2 years ago
Best ResponseYou've already chosen the best response.0so would you use u=cost and du=sint ?

meggiesmermaid
 2 years ago
Best ResponseYou've already chosen the best response.0or could you do \[sint(\cos^2t1)\] which becomes \[\sin^3t\] ?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1and how to you propose to integrate that?

meggiesmermaid
 2 years ago
Best ResponseYou've already chosen the best response.0\[512\int\limits_{1}^{1} 2u^2du  du \] ?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1oh wait, how did 512 get negative?

meggiesmermaid
 2 years ago
Best ResponseYou've already chosen the best response.0im confused because du=sint and the sint is positive so (1/1) would need to be multiplied right?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1yeah, but you already covered that by changing thethe signs og the terms

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1however the double du notation is highly unorthodox and looks screwy to me, so I'd avoid it

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1\[512\int_0^\pi2\cos^2t\sin t\sin tdt\]\[u=\cos t\implies du=\sin tdt\]\[512\int_{1}^{1} 2u^2du +\int_1^{1} \sin tdt\]

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1sorry I messed up the bounds on the last integral, they should be 0 to pi

meggiesmermaid
 2 years ago
Best ResponseYou've already chosen the best response.0and the answer is 1706.66666666667?

meggiesmermaid
 2 years ago
Best ResponseYou've already chosen the best response.0nevermind thats wrong.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1\[512\int_0^\pi2\cos^2t\sin t\sin tdt\]\[u=\cos t\implies du=\sin tdt\]\[512\int_{1}^{1} 2u^2du +\int_0^{\pi} \sin tdt\]let me see what I get...

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1\[512\left(\left.\frac23u^3\right_1^{1}+\left.\cos t\right_0^\pi\right)\]\[512(\frac432)=512(\frac23)\]but I always could have made a mistake...

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1sweet, I just hope you find your (likely algebrabased) mistake

meggiesmermaid
 2 years ago
Best ResponseYou've already chosen the best response.0thats what i got to too! thanks so much!
Ask your own question
Sign UpFind 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.