carilqh persamaan fungsi mula bila:

integral
f(x) = ∫ f '(x) dx

1.
f" (x) = 3x² - 4x + 2 dan  f '(-2)= 3
f '(x)= ∫ f "(x) dx
f '(x) = ∫ 3x² - 4x + 2 dx = x³  - 2x²  + 2x + c
f '(-2)= 3 → (-2)³ - 2(-2)² + 2(-2) + c = 3
-8 - 8 - 4 + c= 3
c = 23

f' (x)= x³ - 2x² + 2x + 23
f(x)= ∫ f '(x)  dx → f(x) = 1/4  x⁴ - 2/3 x³ + x² + 23 x + c
f(1)= 5 →1/4 - 2/3 + 1 + 23 +c = 5
c = -18 ⁷/₁₂
f(x) = 1/4 x⁴ - 2/3 x³ + 23x - 18 ⁷/₁₂
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dy./dx  = 6x² - 4x + 1
y=∫ dy/dx  = ∫6x² - 4x + 1 dx
y = 3x³ - 2x² + x + c
melalui (3, -1)
3 = 3(-1)³ -2(-1)² +(-1)+ c
3 = -3 - 2 -1+c
c= 9
y= 3x³ - 2x² + x+ 9