Using integration find the area of the triangular region whose sides have equations y = 2x +1, y = 3x +1 and x = 4.

To find the point of intersection equate the values of y to get,

2x + 1 = 3x + 1

⇒ x = 0

So, y = 3(0) + 1

= 1

Now when x = 4,

Y = 3(4) + 1

= 12+ 1

= 13

Also, when x = 4,

Y = 2(4) + 1

= 8 + 1

= 9

Hence the points of intersection are (0,1),(4,9),(4,13).

Area ACB = Area OLBAO – Area OLCAO

{The limits for both the brackets are 0 to 4}

= (24 + 4) - (16 + 4)

= 8 units

Hence the required area is 8 square units.