The area (in sq. units) of the part of the circle x²+y²=169 which is below the line 5 x-y=13 is (π α)/(2 β)-65/2+(α)/(β) sin ⁻¹(12/13), where α, β are coprime numbers. Then α+β is equal to _ _ _ _ _.

Integral Calculus: JEE Main 2024 Mathematics question

JEE Main 2024 · 29 Jan, Morning shift · Q31

JEE Main 202429 Jan, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

The area (in sq. units) of the part of the circle

x^2+y^2=169

which is below the line

5 x-y=13

\frac{\pi \alpha}{2 \beta}-\frac{65}{2}+\frac{\alpha}{\beta} \sin ^{-1}\left(\frac{12}{13}\right)

, where

\alpha, \beta

are coprime numbers. Then

\alpha+\beta

is equal to __________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2024 Integral Calculus Question with Answer (29 Jan Morning shift, Q31) | JEE Arc