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]


Say,








And,







So the enclosed area of the triangle is.


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