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MathsMediumMCQ2023 Β· 31 Jan Shift 1

Q77.Let a differentiable function 𝑓 satisfy 𝑓π‘₯+ ∫3 𝑑𝑑𝑑= √π‘₯+ 1, π‘₯β‰₯3. Then 12𝑓8 is equal to: (1) 34 (2) 19 (3) 17 (4) 1

What This Question Tests

This question involves evaluating a definite integral requiring trigonometric substitution, specifically converting sine and cosine terms into half-angle tangent forms, followed by logarithmic integration.

Concepts Tested

Definite integrationSubstitution methodTrigonometric identities

Formulas Used

∫f'(x)/f(x) dx = ln|f(x)|

sin(x) = 2tan(x/2)/(1+tan^2(x/2))

cos(x) = (1-tan^2(x/2))/(1+tan^2(x/2))

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