JEE Main 2024 Mathematics question
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)) makes angle π/6 and π/4, respectively with positive x-axis. If , where α, β are integers, then the value of α + β equal
Answer: (D)
Solution
f′(1) = tan(π/6) = 1/√3 and f′(3) = tan(π/4) = 1. Put u = f′(t): the integral becomes
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