A continuous function satisfies on and on

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Integrals · Applications of Integrals

Problem

A continuous function

g

satisfies

g(x)\ge 0

[0,3]

and

g(x)\le 0

[3,6]

. The area of the region between the graph of

g

and the

x

-axis is

4

square units on

[0,3]

and

6

square units on

[3,6]

. Find the value of

\displaystyle\int_{0}^{6} g(x)\,dx