Diketahui F'(x) = 1/√x + √x dan F(4) = 9, jika F'(x) turunan dari F(x), maka F(x) = ...

turunan dan integral

f'(x)= 1/√x  + √x
f '(x)= x⁻¹/²  + x¹/²

F(x)= ∫ f '(x) dx
F(x) =  2 x¹/²  + ²/₃ x³/² + c
F(x) = 2√x + ²/₃ x √x + c
F(4)=  9 --> 2√4  + ²/₃ (4) √4 + c = 9
2(2) + 8/3(2) + c = 9
4 + 16/3 + c = 9
c = 9-4 -16/3
c = - 1/3

F(x) = 2√x  + ²/₃  x√x - 1/3
F(x) = 1/3 (6x + 2x√x -1)