Using integration, find the area of the region bounded by the triangle ABC whose vertices A, B, C are ( – 1,1), (0,5) and (3,2) respectively.
We have to find the area of the triangle whose vertices are A( – 1,1), B (0,5), C(3,2) as shown below.
The equation of AB,
Y = 4x + 5 ...(i)
The equation of BC,
Y = 5 – x ...(ii)
The equation of AC,
Now the required area(A) =
[(Area between line AB and x - axis) - (Area between line AC and x - axis) from x = - 1 to x = 0]
+ [(Area between line BC and x - axis) - (Area between line AC and x - axis) from x = 0 to x = 3]
So the enclosed area of the triangle is.