Let Vf -2xe two ways sin(y) i+ecos(y)j. Find the change in f between (0,0) and Let Vf

Let Vf -2xe two ways sin(y) i+ecos(y)j. Find the change in f between (0,0) and

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Let Vf -2xe two ways sin(y) i+ecos(y)j. Find the change in f between (0,0) and (1,/2) in (a) First, find the change by computing the line integralVf dr, where C is a curve connecting (0,0) and (1,/2) The simplest curve is the line segment joining these points. Parameterize it: with 0 s t 1,7() So that Vf di 7+ dt Note that this isn't a very pleasant integral to evaluate by hand (though we could easily find a numerical estimate for it). It's easier to find Vf dr as the sum Vf dř, where C is the line Jc Vf di e segment from (0,0) to (1,0) and C2 is the line segment from (1,0) to (1,/2). Calculate these integrals to find the change in f Vf df= So that the change inf c Vf.7= c Vf di + e Vf.df (b) By computing values of f. To do this First find f(x, y) Thus f(0,0) and f(1,/2) and the change in f is Let Vf -2xe two ways sin(y) i+ecos(y)j. Find the change in f between (0,0) and (1,/2) in (a) First, find the change by computing the line integralVf dr, where C is a curve connecting (0,0) and (1,/2) The simplest curve is the line segment joining these points. Parameterize it: with 0 s t 1,7() So that Vf di 7+ dt Note that this isn't a very pleasant integral to evaluate by hand (though we could easily find a numerical estimate for it). It's easier to find Vf dr as the sum Vf dř, where C is the line Jc Vf di e segment from (0,0) to (1,0) and C2 is the line segment from (1,0) to (1,/2). Calculate these integrals to find the change in f Vf df= So that the change inf c Vf.7= c Vf di + e Vf.df (b) By computing values of f. To do this First find f(x, y) Thus f(0,0) and f(1,/2) and the change in f is

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