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Application of Integrals
NCERT Class 12
CBSE
Grade 12

Question:

Using integration, find the area of the region bounded by the lines $x + 2y = 2, y - x = 1$ and $2x + y = 7$.

Step-by-Step Solution

Find vertices $A(0,1), B(2,3), C(4,-1)$. [1.5 Marks]
$\text{Area} = \int_0^2 \dfrac{3x}{2} dx + \int_2^4 \left( 6 - \dfrac{3x}{2} \right) dx$. [2.0 Marks]
$= 3 + 3 = 6$ sq. units. [1.5 Marks]

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🎯 Official CBSE Marking Scheme:
Evaluating 3 intersection points of boundary lines: 1.5 Marks
Formulating 2-part area integrals: 2.0 Marks
Evaluating total area $= 6$ sq. units: 1.5 Marks

Correct Answer:
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