Since fy(x, y) = x², find f(x, y). f(x, y) = + g(y)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider F and C below.
F(x, y) = x2 i + y² j
C is the arc of the parabola y = 3x2 from (-2, 12) to (-1, 3)
Exercise (a)
Find a function f such that F = Vf.
Step 1
If Vf(x, y) = F(x, y) = x²i + y²j, then
fx(x, y) = x2
and
fy(x, y) =
Step 2
Since f(x, y) = x², find f(x, y).
f{x, у) -
+ g(y)
Transcribed Image Text:Consider F and C below. F(x, y) = x2 i + y² j C is the arc of the parabola y = 3x2 from (-2, 12) to (-1, 3) Exercise (a) Find a function f such that F = Vf. Step 1 If Vf(x, y) = F(x, y) = x²i + y²j, then fx(x, y) = x2 and fy(x, y) = Step 2 Since f(x, y) = x², find f(x, y). f{x, у) - + g(y)
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