Calculate F(12) given that F(9) = 3 and F '(x) = x^2. Hint: Express F(12) − F(9) as a definite integral.

Question

Show me how it's done, smart people.

Answer 1

F'(x) = x^2

Integrating...

F(x) = (1/3)X^3 + C

3 = F(9) = (1/3)*9^3 + C

3 = (1/3)9^3 + C

3 = (1/3)(9*9*9) + C

3 = 3*9*9 + C

3 = 243 + C

C=-240

f(x) = (1/3)X^3 - 240

f(12) = 1/3)(12*12*12)- 240 =1488