Simple line integral problem I cant seem to get

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SUMMARY

The discussion centers on evaluating the line integral of the function (2x + y)dx + xydy along the curve defined by y = x + 3, between the points (-1, 2) and (2, 5). The initial approach incorrectly parametrized the curve by x for both segments of the integral, leading to confusion regarding the limits of integration. The correct method involves ensuring that the parametrization is consistent with the curve's equation and the corresponding limits for both x and y.

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gr3g1
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I have to evaluate the line integral :
[itex]\oint_{}^{} (2x + y)dx + xydy[/itex] between (-1,2) and (2,5)

on the curve: [itex]y = x + 3[/itex]

So, what I did was:
[itex]\int_{-1}^{2} (3x+3)dx + \int_{2}^{5} (x^{2} + 3x)dx[/itex]

However, this is wrong and I am not sure why!
Can someone please guide me?
Thanks a lot!
 
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You are parametrizing the curve by the value of x which goes from -1 to 2. In BOTH parts. Since you've expressed the dy part of the integral in terms of x, why are you using the y limits there?
 
Ahhh, thanks so much!
 

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