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  • Using integration, find the area of the region <img alt="{(x, y) : x^{2} + y^{2} \leq 9, x + y \geq 3}." src="https://learn.careers360.com/latex-image/?%7B%28x%2C%20y%29%20%3A%20x%5E%7B2%7D%20&plus;%20y%5E%7B2%7D%20%5Cleq%209%2C%20x%20&plu

Using integration, find the area of the region {(x, y) : x^{2} + y^{2} \leq 9, x + y \geq 3}.

 

 

Answers (1)

{(x, y) : x^{2} + y^{2} \leq 9, x + y \geq 3}.

$ Required Area = Area of AMB

Point A(0,3)

Point A(3,0)

\\ $ ar( AMB) $ =\int_0^3 (\sqrt{9-x^2}-(3-x))dx \\ = [\frac{x}{2} \sqrt{9-x^2}+ \frac{9}{2} \sin ^{-1}\frac{x}{3}- 3x + \frac{x^2}{2}]_0^3 \\\\ = [0 + 9 \pi - 9 + \frac{9}{2} - 0-0-0-0] \\\\ = 9\pi - \frac{9}{2}

 

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Safeer PP

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