JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

If the value of the integral

\int_0^5 {\frac{{X + \left[ X \right]}}{{{e^{x - \left[ X \right]}}}}} dx = \alpha {e^{ - 1}} \times \beta

, where

\alpha ,\,\,\beta \in R,\,\,5\alpha + 6\beta = 0

and

[X]

denotes the greatest integer less than or equal to

x

, then the value of

{\left( {\alpha + \beta } \right)^2}

is equal to:

View answer and explanation

Correct option: B

Option B (25) is correct because after evaluating the integral and using the given condition

5\alpha + 6\beta = 0

, we find that

(\alpha + \beta)^2 = 25

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