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ranyai12
Group Title
Evaluate the line integral 5ydx+2xdy where C is the straight line path from (4,4) to (7,8)
 one year ago
 one year ago
ranyai12 Group Title
Evaluate the line integral 5ydx+2xdy where C is the straight line path from (4,4) to (7,8)
 one year ago
 one year ago

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ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
I got 276 but was wrong
 one year ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
@Hero please help!
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.1
\[\int_C (5y~dx+2x~dy)\] The line connecting (4,4) and (7,8) is \(y=\dfrac{4}{3}x\dfrac{4}{3}\) Parameterize \(C\) by \[\begin{cases}x=t\\ \\ y=\dfrac{4}{3}t\dfrac{4}{3}\\ \\ 4<t<7 \end{cases}\] So you have \(dx=dt\) and \(dy=\dfrac{4}{3}dt\): \[\int_4^7 \bigg[5\left(\dfrac{4}{3}t\dfrac{4}{3}\right)~dt+2t~\left(\dfrac{4}{3}dt\right)\bigg]\\ \int_4^7\bigg[\frac{28}{3}t\frac{20}{3}\bigg]~dt\\ ~~~~~~~~~~~~~~~~\vdots\]
 one year ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
did you get 134?
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.1
Yep: http://www.wolframalpha.com/input/?i=Integrate%5B%2828%2F3%29*t%2820%2F3%29%2C%7Bt%2C4%2C7%7D%5D Can't guarantee that's the right answer, but that's what my method is getting, so I'm sticking with it.
 one year ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
when i did it by hand, i ended up getting 288
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.1
Could you show your work? It might be a mistake in the integration, or the parameterization.
 one year ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
288 is wrong :(
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.1
Well what did you do when you tried it? How did you parameterize \(C\)?
 one year ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
no i integrated wrong! the answer is indeed 134
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.1
Oh ok then.
 one year ago

ranyai12 Group TitleBest ResponseYou've already chosen the best response.0
Thanks so much
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.1
You're welcome!
 one year ago
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