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Using integration find the area of the triangle ABC whose vertices are A(3,0), B(4,6) and C(6,2)

Using integration find the area of the triangle ABC whose vertices are A(3,0), B(4,6) and C(6,2)

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
i)Area of an enclosed region bounder by the curve y = f(x), x-axis and the boundaries,x = a to b is given by A = ∫f(x) dx in [x = a to b]
ii) Hence, here the area of the triangle ABC is enclosed by the lines AB, BC & CA; its area byintegrationis given by Area under AB + Area under BC - Area under AC
iii) Using two point form equation of AB, Bc & CA are respectively:
y = 6(x -3); y-6 = -2(x-4) and y = (2x - 6)/3
iv) Area under AB = ∫(6x - 18) dx in [3 to 4] = ([6x²/2 - 18x] in [3 to 4]
Evaluating for the limits, A1 = 3
Similarlyarea under BC = (14x - x²) in [4 to 6] = 8
Area under AC = (x²/3 - 2x) in [3 to 6] =3
Hence net area = 3+ 8 - 3 = 8 sq units.
Thanks and Regards
Shaik Aasif
askIITians faculty

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