Let be a polynomial function whose derivative is

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

Let

G(x)

be a polynomial function whose derivative is

G'(x)=kx^2+6x

, where

k

is a constant. (i) Find the general form of

G(x)

in terms of

k

and the constant of integration

C

. (ii) Given the two conditions

G(1)=5

and

G(2)=15

, determine the values of

k

and

C

. (iii) Write the complete expression for

G(x)

using the values of

k

and

C

obtained in part (ii).