Application of Integrals Question - CBSE

Question

Using integration, find the area of the region bounded by the triangle whose vertices are $(1, 0), (2, 2)$ and $(3, 1)$.

Accepted Answer

Equations of lines: $AB: y = 2(x-1), BC: y = 4-x, AC: y = \dfrac{x-1}{2}$. [1.5 Marks]
$ ext{Area} = \int_1^2 \left[ 2(x-1) - \dfrac{x-1}{2} ight] dx + \int_2^3 \left[ (4-x) - \dfrac{x-1}{2} ight] dx$. [2.0 Marks]
$= \dfrac{3}{4} + \dfrac{3}{4} = \dfrac{3}{2}$ sq. units. [1.5 Marks]

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🎯 Official CBSE Marking Scheme:
Finding equations of 3 boundary lines: 1.5 Marks
Formulating 2-part definite integrals: 2.0 Marks
Evaluating total triangular area $= 3/2$ sq. units: 1.5 Marks

Question:

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