Jika f'(x)=x^2+2x dan f(1)=3 maka f(x)=

Jika f'(x)=x^2+2x dan f(1)=3 maka f(x)=

$f'(x)=x^2+2x \ f(x) = int(x^2+2x)dx \ f(x) = frac{1}{2 + 1} {x}^{2 + 1} + frac{2}{1 + 1} {x}^{1 + 1} + c \ f(x) = frac{1}{3} {x}^{3} + {x}^{2} + c \ f(1) = frac{1}{3} {(1)}^{3} + {(1)}^{2} + c \ 3 = frac{1}{3} + 1 + c \ c = 2 - frac{1}{3} \ c = frac{5}{3} \ f(x) = frac{1}{3} {x}^{3} + {x}^{2} + frac{5}{3}$