Let y=f(x) be a thrice differentiable function in (-5,5). Let the tangents to the curve y=f(x) at (1, {\f}(1 )) and (3, {\f}(3 )) make angles \frac{\pi}{6} and \frac{\pi}{4}, respectively with positive x-axis. If 27 \int_{1}^{3} ( (f^{'}(t)) ^2+1) {\f}^{' '}( {\t}) {\dt}=\alpha+\beta \sqrt{3} where \alpha, \beta are integers, then the value of \alpha+\beta equals [30-Jan-2024 Shift 2]

JEE Main 30-Jan-2024 Shift 2 Solved Paper

Section: Mathematics

Question : 9 of 90

Marks: +1, -0

Let y=f(x) be a thrice differentiable function in (−5,5). Let the tangents to the curve y=f(x) at (1, f(1)) and (3,f(3)) make angles ‌

and ‌

, respectively with positive x-axis. If 27‌

∫

((f′(t))2+1)f′′(t)‌dt=α+β√3‌‌ where ‌‌α,‌‌β are integers, then the value of α+β equals

[30-Jan-2024 Shift 2]

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