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meggiesmermaid
Group Title
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.
 2 years ago
 2 years ago
meggiesmermaid Group Title
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.
 2 years ago
 2 years ago

This Question is Closed

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

meggiesmermaid Group TitleBest 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.
 2 years ago

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

meggiesmermaid Group TitleBest ResponseYou've already chosen the best response.0
so du =sinx
 2 years ago

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

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

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

meggiesmermaid Group TitleBest 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
 2 years ago

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

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

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

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

meggiesmermaid Group TitleBest ResponseYou've already chosen the best response.0
oh yeah.haha.
 2 years ago

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

meggiesmermaid Group TitleBest ResponseYou've already chosen the best response.0
i mean + du
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
yeah, looks good
 2 years ago

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

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

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

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

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

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

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

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

TuringTest Group TitleBest 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...
 2 years ago

TuringTest Group TitleBest 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...
 2 years ago

meggiesmermaid Group TitleBest ResponseYou've already chosen the best response.0
its right! yay!
 2 years ago

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

meggiesmermaid Group TitleBest ResponseYou've already chosen the best response.0
thats what i got to too! thanks so much!
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
welcome!
 2 years ago
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