(Antiderivatives – Constant of Integration)
Answer all parts.
a. (i) Define an antiderivative (indefinite integral) of a function f(x).
b. (ii) Explain, with reason, why an arbitrary constant must be added while writing the most general antiderivative of a function.
c. (iii) If F(x) is any one antiderivative of f(x), show that F(x)+k is also an antiderivative of f(x) for every real constant k.