Application of Integrals Question - CBSE

Question

Find the area of the smaller region bounded by the circle $x^2 + y^2 = 4$ and the line $x + y = 2$.

Accepted Answer

$ ext{Area} = \int_0^2 [\sqrt{4-x^2} - (2-x)] dx$. [2.0 Marks]
$= \left[ \dfrac{x}{2}\sqrt{4-x^2} + 2\sin^{-1}(x/2) - 2x + \dfrac{x^2}{2} ight]_0^2$. [1.5 Marks]
$= \pi - 2$ sq. units. [1.5 Marks]

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🎯 Official CBSE Marking Scheme:
Formulating difference integral between circle and line: 2.0 Marks
Applying standard integration formulas: 1.5 Marks
Evaluating area $= \pi - 2$ sq. units: 1.5 Marks

Question:

Step-by-Step Solution

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