Practice question · Numerical answer
A function F satisfies F'(x) = 3x^2 and F(1) = 10. Compute F(3).
Hints
- Antidifferentiate to x^3 + C, then use the known value to find C.
- F(1) = 1 + C = 10.
Show the answer
36
Why
C = 9, so F(3) = 27 + 9 = 36. Forgetting the constant gives 27, and a nine-unit error that no amount of correct antidifferentiation can repair. The constant is not decoration; it carries real information.
Practise Integration and Antiderivatives
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