The required area is the triangle bonded between the three lines\[y+2x+1----(1),y=3x+1-----(2),and \;x=4------(3).\]
Let us solve these equations to get the vertices of the triangle formed.
To find the vertex A,let us solve equ(1)&(2),\[y=2x+1,y=3x+1\]
2x+1=3x+1 $\Rightarrow x=0,y=1.$
Hence vertex A is (0,1)
To find the vertex B let us solve the equ(2)&(3),
vertex B is (4,13)
To find the vertex C,let us solve equ(3)&(1)
vertex C is (4,9).
Now the required area of the triangle is the shaded portion as shown in the fig.
On integrating we get,
On applying limits we get,
Hence the required area is 8 sq. units.