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Question: Indefinite integral for two variables

Question:Indefinite integral for two variables

janhardo 335 Maple
integration indefinite
September 21 2020
0

Maple is not adding a function g(y) to the indefinite integral 
Maybe i do miss here something ?
 

int(2*x*y, x)

x^2*y

 (1)

textbook  f(x, y) = int(f[x](x, y), x) and int(f[x](x, y), x) = int(2*x*y, x) and int(2*x*y, x) = x^2*y+g(y)f(x, y) = int(f[x](x, y), x)

f(x, y) = int(f[x](x, y), x)

 (2)

int(2*x*y, x) = x^2*y+g(y)

x^2*y = x^2*y+g(y)

 (3)

looks like the y is constant  in f(x,y)
Maple is not putting a constant with the integral int(f, x)  , the same for int(2*x*y, x)
Think then only the integrand 2x is integrated and y is a constant, but the notation of g(y) is not C  

 

Integral  x^2*y+g(y)and then  partieel differentation gives  2x.y  

Its about finding a potential function for a vectorfield F

 

 

NULL


 

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