Jika diketahui f'(x)=x-√x dan f(4)=-3 maka tentukan f(x)

jawab

f ' (x) = x - √x

f(x) = ∫ f '(x )  dx
f(x) = ∫  (x  - √x) dx
f(x) = 1/2 x² - 2/3 x^(3/2)  + c
f(x)  = 1/2 x² - 2/3 x√x +  C
f(4) = 3
1/2 (4²)  - 2/3 (4√4) + c = -3
8 - 16/3 + c = -3
c = - 5 ²/₃
f(x) = 1/2 x² + 2/3  x√x  - 5 ²/₃