JEE Main 2006Annual, Paper 1MathematicsMediumIntegral Calculus369× since 2002The value of ∫1a[x]f′(x)dx,a>1\int\limits_1^a {\left[ x \right]} f'\left( x \right)dx,a > 11∫a[x]f′(x)dx,a>1 where [x]{\left[ x \right]}[x] denotes the greatest integer not exceeding xxx isAOption A. af(a)−{f(1)+f(2)+.............f([a])}af\left( a \right) - \left\{ {f\left( 1 \right) + f\left( 2 \right) + .............f\left( {\left[ a \right]} \right)} \right\}af(a)−{f(1)+f(2)+.............f([a])}BOption B. [a]f(a)−{f(1)+f(2)+...........f([a])}\left[ a \right]f\left( a \right) - \left\{ {f\left( 1 \right) + f\left( 2 \right) + ...........f\left( {\left[ a \right]} \right)} \right\}[a]f(a)−{f(1)+f(2)+...........f([a])}COption C. [a]f([a])−{f(1)+f(2)+...........f(a)}\left[ a \right]f\left( {\left[ a \right]} \right) - \left\{ {f\left( 1 \right) + f\left( 2 \right) + ...........f\left( a \right)} \right\}[a]f([a])−{f(1)+f(2)+...........f(a)}DOption D. af([a])−{f(1)+f(2)+.............f(a)}af\left( {\left[ a \right]} \right) - \left\{ {f\left( 1 \right) + f\left( 2 \right) + .............f\left( a \right)} \right\}af([a])−{f(1)+f(2)+.............f(a)}CheckSkip · show solution
