Tentuka fungsi F(x) jika diketahui F'(x)=x3-x2 dan F(2)= 9/4

F(x) = Integral x³ - x²
= ¼x⁴ - ⅓x³ + C

Diketahui
F(2) = 9/4
¼.2⁴ - ⅓.2³ + C = 9/4
¼.16 - ⅓.8 + C = 9/4
4 - 8/3 + C = 9/4
C = 9/4 + 8/3 - 4
C = (27+32-48)/12
C = 11/12

Jadi, F(x) = ¼x⁴ - ⅓x³ + 11/12

dik : F'(x)=X^3-X^2, F(2)=9/4
dit : F(x)....?

Penye :
F(x) = integral F'(x) dx
F(x) =integral (X^3-X^2)dx
        = 1/4x^4-1/2x^2+c
F(2)=9/4
 F(2)=1/4(2)^4-1/2(2)^2+c=9/4
        = 4-2+c=9/4
        = 2+c=9/4
               c = 9/4-2
                  =1/4
jadi F(x)= 1/4x^4-1/2x^2+1/4