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Area Under the Curves question

2024 · 29 Jan · Shift 1 · Q51
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Area Under the Curves question

2024 · 29 Jan · Shift 1 · Q51

JEE MainMathematicsArea Under the CurvesNumerical+4 / −1
The area (in sq. units) of the part of the circle x2+y2=169x^2+y^2=169x2+y2=169 which is below the line 5x−y=135 x-y=135x−y=13 is πα2β−652+αβsin⁡−1(1213)\frac{\pi \alpha}{2 \beta}-\frac{65}{2}+\frac{\alpha}{\beta} \sin ^{-1}\left(\frac{12}{13}\right)2βπα​−265​+βα​sin−1(1312​), where α,β\alpha, \betaα,β are coprime numbers. Then α+β\alpha+\betaα+β is equal to ‾\underline{\hspace{2cm}}​.
Numerical answer
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