JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

The integral

\int\limits_0^1 {\frac{1}{{{7^{\left[ {\frac{1}{x}} \right]}}}}} dx,

where

\left[ \cdot \right]

denotes the greatest integer function, is equal to

View answer and explanation

Correct option: A

1 + 6{\log _e}\left( {\frac{6}{7}} \right)

The correct answer is A (

1 + 6{\log _e}(\frac{6}{7})

) because it is the result of evaluating the given definite integral using substitution and properties of logarithms.

More Questions from DEFINITE INTEGRATION

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\int \nolimits_0^\infty \,\,\log \,\,\left( {x + \frac{1}{x}} \right)\,\,\frac{{dx}}{{1 + {x^2}}}

f\left( x \right)

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f\left( {\frac{4}{{25}}} \right)

\int\limits_{{0}}^{11}[x]^{3} . \mathrm{dx}

[*]

\int\limits_{2}^4 \frac{\log x^2}{\log x^2+\log \left(36-12 x+x^2\right)} d x

\int\limits_{{-2}}^0\left(x^3+3 x^2+3 x+3+(x+1) \cos (x+1)\right) d x

I\,\,\left( {m,\,\,n} \right) = \int \nolimits_0^1 \,\,{t^m}\,\,{\left( {1 + t} \right)^n}\,\,dt

I\left( {m,\,\,n} \right)

I\,\,\left( {m + 1,\,\,n + 1} \right)