9. Let f(x,y)=2+²+2y2j for all (x, y) # (0,0), and C: x= cost, y = sint, 0≤ t ≤ 2. (a) Show that f= VF, for F(x, y) = tan-¹(y/x). (b) Show that ff. dr = 27.
9. Let f(x,y)=2+²+2y2j for all (x, y) # (0,0), and C: x= cost, y = sint, 0≤ t ≤ 2. (a) Show that f= VF, for F(x, y) = tan-¹(y/x). (b) Show that ff. dr = 27.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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9. Let f(x,y)= wifyi+x+yjfor all (x,y) ≠ (0,0), and C: x = cost, y = sint, 0 ≤ t <2π.
(a) Show that f = VF, for F(x,y) = tan-1(y/x).
(b) Show that f-dr=2π.
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