Find ∫ 3/2 15 ⌊ ln ⌊ x ⌋⌋ d x , where ⌊ ⋅ ⌋ is the greatest-integer function.

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MathematicsDefinite IntegrationMiscellaneous/MixedMedium2 minQB

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Find $\int_{3/2}^{15} ⌊ ln ⌊ x ⌋⌋ d x$ , where $⌊ \cdot ⌋$ is the greatest-integer function.

Answer:

Solution:

$⌊ ln ⌊ x ⌋⌋$ is 0 on [3/2, 3), 1 on [3, 8), and 2 on [8, 15]. Thus the integral is $5 + 14 = 19$ .

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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