Answer:
f = tanx *i + y³*j
Step-by-step explanation:
F(x,y) = ??
Fx,y) = gradf
Then
f(x,y) = ∫ sec²x dx + ∫ 3y²dy
∫ sec²x dx = ∫ 1/ cos²x dx
By change of variables
if z = tan x then z = sinx/cosx
dz/dx = cosx*cosx - (-sinx*sinx) / cos²x
dz/dx = cos²x + sin²x /cos²x
dz/dx= 1 /cos²x
dz = dx/ cos²x
∫ 1/ cos²x dx = ∫dz = z = tanx
And ∫3*y² = y³
Then f = tanx *i + y³*j
