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Problem 40 Hard Difficulty

Given the force field $\mathbf{F}$, find the work required to move an object on the given oriented curve.
$\mathbf{F}=\langle x, y\rangle$ on the path consisting of the line segment from (-1,0) to (0,8) followed by the line segment from (0,8) to (2,8)

Answer

$$\frac{67}{2}$$

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Video Transcript

All right. Number 40 Given the force field F vehicles X y find the line integral Following the path I'm gonna welcome 0 to 0 comma eight and then zero comma eight to to come eight So we can fire Our friends are are on to you real quick So starts Ah, negative one No good warning zero. And we got 8 to 0. My single one is one's won t eight more zeros A So a t is equal to a good one plus t comma 80 our prime if t is one coming, not put everything into are in agro that equals integral from 0 to 1 negative one plus t come a ti dot With one comedy t t go to in the girl from 0 to 1 of negative one of 65 t t t which is equal to negative t plus 65 t squared over two evaluated from 0 to 1 giving a 63 over to No, the second part moving from zero comma eight to to come eight. So our new parametric is from zero. Come on a moves to companies or two come to mind zeros two plus two t 81 is 80 plus zero t. So it's to t comma A are prying physical toe to coma zero plug it into the same in agro from 0 to 1 to g comma a uh to come a zero t t. And this is a good A for T squared over two from zero, while which skirted too. So then we have 63/2 plus two, which is equal to 67 or two.

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