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Definite Integration question

2006 · Shift 0 · Q54

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PYQ Library
JEE Main
Mathematics
Definite Integration
2006 · Shift 0 · Q54

Definite Integration question

2006 · Shift 0 · Q54

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

The value of

\int\limits_1^a {\left[ x \right]} f'\left( x \right)dx,a \gt 1

where

{\left[ x \right]}

denotes the greatest integer not exceeding

x

is

A
$af\left( a \right) - \left\{ {f\left( 1 \right) + f\left( 2 \right) + .............f\left( {\left[ a \right]} \right)} \right\}$
B
$\left[ a \right]f\left( a \right) - \left\{ {f\left( 1 \right) + f\left( 2 \right) + ...........f\left( {\left[ a \right]} \right)} \right\}$
C
$\left[ a \right]f\left( {\left[ a \right]} \right) - \left\{ {f\left( 1 \right) + f\left( 2 \right) + ...........f\left( a \right)} \right\}$
D
$af\left( {\left[ a \right]} \right) - \left\{ {f\left( 1 \right) + f\left( 2 \right) + .............f\left( a \right)} \right\}$

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