Here's the question you clicked on:
ranyai12
Evaluate the line integral 5ydx+2xdy where C is the straight line path from (4,4) to (7,8)
I got 276 but was wrong
\[\int_C (5y~dx+2x~dy)\] 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 \(dy=\dfrac{4}{3}dt\): \[\int_4^7 \bigg[5\left(\dfrac{4}{3}t-\dfrac{4}{3}\right)~dt+2t~\left(\dfrac{4}{3}dt\right)\bigg]\\ \int_4^7\bigg[\frac{28}{3}t-\frac{20}{3}\bigg]~dt\\ ~~~~~~~~~~~~~~~~\vdots\]
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.
when i did it by hand, i ended up getting 288
Could you show your work? It might be a mistake in the integration, or the parameterization.
Well what did you do when you tried it? How did you parameterize \(C\)?
no i integrated wrong! the answer is indeed 134
You're welcome!