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Problem 4 Medium Difficulty

Evaluate the line integral, where $ C $ is the given curve.

$ \displaystyle \int_C xe^y \, ds $, $ C $ is the line segment from $ (2, 0) $ to $ (5, 4) $

Answer

$$
\frac{85 e^{4}-25}{16}
$$

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Video Transcript

Okay, Another light on your problem. We first Paramount rice and line segment. So this one x should be to prosperity. Why should be forty and t goes from zero to what? So this is like a standard perma translation on the second. And after that, we just publicly and less computer yes, square root off the X ditty square plus square, which is five teams. So here goes from zero to one. Access to plus treaty wise Fortin and D s is five snowless expended Wish we had a tendency to the forty plus fifteen fourteen and uh, no everybody, he's here to try to derive the form. Laugh off this first. So that's the first set up a problem like this. If you remember the entire the review of this, this will be good. But if you don't, we just do integration by part to figure that out first. So just eat with the forty. This one's easy. I buy you some tissues or anything you like pussy. This one I have to be careful. No, I said this to be Hugh this TV that we should get you times minus into grow offi you is therefore let me write it here. Four over for my ass. Sorry, it's called B Down the problem and TV to the forty. The fourth should be is the forty or for minus the last interview. Just finish it. Eat forty over sixteen. Oh, and plus a constant. So as continue the origin of para you want to compute it's girl. So So the original problem with oil The computer into growth from zero to one and either the forty plus fifteen you to the forty three. So this will be zero to what? So this should be ten over four five over Tui's Fortin plus our fifteen times thiss so fifteen t eat with fourteen over for minus fifteen over sixteen. It was the forty, and, uh, this is forty over. This is forty over sixteen and you combine the first German last time together. I should get plus twenty five No, over six hundred forty, then we probably want probably when we get fifteen meters for over four plus twenty five over sixteen to four and we're probably zero first. How is zero and seven? Term is twenty five over sixteen. So yes, further simplified. This is six this sixty over sixteen So eighty five over sixteen with a forest minus twenty five over sixteen