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

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

SithsAndGiggles
 one year ago
Best 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 \(dy=\dfrac{4}{3}dt\): \[\int_4^7 \bigg[5\left(\dfrac{4}{3}t\dfrac{4}{3}\right)~dt+2t~\left(\dfrac{4}{3}dt\right)\bigg]\\ \int_4^7\bigg[\frac{28}{3}t\frac{20}{3}\bigg]~dt\\ ~~~~~~~~~~~~~~~~\vdots\]

SithsAndGiggles
 one year ago
Best ResponseYou've already chosen the best response.1Yep: 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.

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

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

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

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

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