Question

→ (1 point) Let Vf-6xe-r sin(5y) +1 5e* cos(Sy) j. Find the change inf between (0,0) and (1, n/2) in two ways. (a) First, find the change by computing the line integral c Vf di, where C is a curve connecting (0,0) and (1, π/2) The simplest curve is the line segment joining these points. Parameterize it: with 0 t 1, K) = 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 /_. V where C1 is the line segment from (0, 0) to (1, 0) and C2 is the line segment from (1,0) to (1, z/2). Calculate these integrals to find the change inf f dio Vf di, C1 So that the change inf-f VfFa Vf dr+ Jsc Vf dr (b) By computing values of f. To do this, First find f(x,y)- Thus and f(1 , π/2) = and the change in f is

Answer 1

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