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Find the work done by the force field $ \textbf{F}(x, y) = x^2 \, \textbf{i} + ye^x \, \textbf{j} $ on a particle that moves along the parabola $ x = y^2 + 1 $ from $ (1, 0) $ to $ (2, 1) $.

Work done $$=\frac{7}{3}+\frac{e^{2}-e}{2}$$

Vector Calculus

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Missouri State University

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so find the work done. So we have the computer into growth. If the e r and the first step is to Paramount tries thiss so because that if wise teeth and access t square pross watts from one to two. So sorry T phones here to what? So then we can compute that have for far off t we repress exploit his square pross wad Replays Why buy t Expect hiss where process and our prime of tea which has taken a component wise so to tea and one so this integral will be the frontier will be taught product of these two So to TT square plus one square plus t e to the T square plus one So no next step It's right out Antiterrorism it Eve. Well, it's not that hard to see that both both parts are some kind of U substitution apartment. If you that t score plus one host you and to Teo ptu So this will be he square plus one cube over Siri plus e to the T Square plus one. Oh, yeah, too. So we have one over two years we'LL take the relative You knew the prostitute E in front. You get this and we plug it in one. We got to to kill witches. Eight eight over three plus one over to times Square. Miners were probably zero. Would you have won over three? No. And you're probably zero. We get minus one over to eat with the one and we can collect. Term together. Seven over three, plus one over to his square, minus e.

Vector Calculus