Mathematics

Problem

For the polynomial function

f(x)=k x^{3}+4

, one antiderivative is denoted by

F(x)

. a. (i) Find the general expression for

F(x)

, leaving the constant of integration as

C

. b. (ii) The curve

y=F(x)

passes through the points

(1,10)

and

(2,30)

. Using these conditions, determine the numerical values of

k

and

C