The region bounded by y=(3x)^(1/2), y=3x-6, y=0

4.5 sq. units.

Step-by-step explanation:

The given curve is

⇒ ...... (1)

This curve passes through (0,0) point.

Now, the straight line is y = 3x - 6 ....... (2)

Now, solving (1) and (2) we get,

⇒ (y - 3)(y + 2) = 0

⇒ y = 3 or y = -2

We will consider y = 3.

Now, y = 3x - 6 has zero at x = 2.

Therefor, the required are =

=

=

= 6 - 1.5

= 4.5 sq. units. (Answer)