Consider the integral $l\, = \,\int\limits_0^{10} {\frac{{\left[ x \right]{e^{\left[ x \right]}}}}{{{e^{x - 1}}}}} {\rm{ }}dx$, Where $[x]$ denotes the greatest integer less than or equal to $x$. Then, the value of $l$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

Consider the integral

l\, = \,\int\limits_0^{10} {\frac{{\left[ x \right]{e^{\left[ x \right]}}}}{{{e^{x - 1}}}}} \mathrm{ }dx

, Where

[x]

denotes the greatest integer less than or equal to

x

. Then, the value of

l

is equal to

View answer and explanation

Correct option: C

45\left( {e-1} \right)

Option C (

45(e-1)

) is correct because the integral can be simplified by breaking it into intervals and using the properties of the greatest integer function.

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