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

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ranyai12Best ResponseYou've already chosen the best response.0
I got 276 but was wrong
 10 months ago

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

SithsAndGigglesBest 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.
 10 months ago

ranyai12Best ResponseYou've already chosen the best response.0
when i did it by hand, i ended up getting 288
 10 months ago

SithsAndGigglesBest ResponseYou've already chosen the best response.1
Could you show your work? It might be a mistake in the integration, or the parameterization.
 10 months ago

SithsAndGigglesBest ResponseYou've already chosen the best response.1
Well what did you do when you tried it? How did you parameterize \(C\)?
 10 months ago

ranyai12Best ResponseYou've already chosen the best response.0
no i integrated wrong! the answer is indeed 134
 10 months ago

SithsAndGigglesBest ResponseYou've already chosen the best response.1
You're welcome!
 10 months ago
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