Consider the function on the interval .

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

Problem

Consider the function

g(x)=x^{3}-6x^{2}+9x

on the interval

0\le x\le5

. (a) Solve

g(x)=0

for

x

in the interval

[0,5]

. (b) Calculate the exact area of the region enclosed by the graph of

g

and the

x

-axis on

[0,5]

. (c) Confirm that your result in part (b) is positive and interpret its meaning in the context of area.