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

Explanation

Equation of the sides of `triangle ABC`,
Let equation of AB is `y=2x+1`
Equation of BC is `y=3x+1`
Equation of AC is `x=4`

Their points of intersection i.e, coordinates of A, B and C respectively are (4, 9), (0, 1) and (4, 13).
Now `ar(triangle ABC)`
`=ar(triangle (ODCBO)-ar(ODABO)`
`=int_(0)^(4)(3x+1)dx-int_(0)^(4)(2x+1)dx`
`=int_(0)^(4)xdx=[(x^(2))/(2)]_(0)^(4)=8` sq. units.