Question

The value of $\mathop \smallint 
olimits_1^a \,\,\left[ x ight]\,\,f'\left( x ight)\,dx,\,\,a > 1$ where $\left[ x ight]$ denotes the greatest integer not exceedingx, is

Accepted Answer

$\left[ a \right]\,\,f\left( a \right)\,\, - \,\,\left\{ {\,\,f\left( 1 \right)\,\, + \,\,f\,\,\left( 2 \right)\,\, + \,\,...\,\, + f\,\,\left( {\left[ a \right]} \right)} \right\}$

Answer

$\left[ a \right]\,\,\,f\,\,\left( {\left[ a \right]} \right)\,\, - \,\,\left\{ {f\,\,\left( 1 \right)\,\, + \,\,f\,\,\left( 2 \right)\,\, + \,\,... + \,\,f\,\,\left( a \right)} \right\}$

Answer

$af\,\,\left( {\left[ a \right]} \right)\,\, - \,\,\left\{ {f\left( 1 \right)\,\, + \,\,f\,\,\left( 2 \right) + \,\,... + \,\,f\left( a \right)} \right\}$

Answer

$af\,\,\left( a \right)\,\, - \,\,\left\{ {f\,\,\left( 1 \right)\,\, + \,\,f\,\,\left( 2 \right) + \,\,...\,\, + f\,\,\left( {\left[ a \right]} \right)} \right\}$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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