Let f:R → R be a differentiable function having f(2) = 6, f'(2) = (1/48). Then lim x → 2 ∫₆^(f(x)) (4t³)/(x - 2)dt equals:

Integral Calculus: JEE Main 2005 Mathematics question

JEE Main 2005 · Annual, Paper 1 · Q3300

JEE Main 2005Annual, Paper 1MathematicsMediumIntegral Calculus369× since 2002

Let

f:R \to R

be a differentiable function having

f\left( 2 \right) = 6

f'\left( 2 \right) = \left( {{1 \over {48}}} \right)

. Then

\mathop {\lim }\limits_{x \to 2} \int\limits_6^{f\left( x \right)} {{{4{t^3}} \over {x - 2}}dt}

equals :

JEE Main 2005 · Annual, Paper 1 · Q3300

JEE Main 2005Annual, Paper 1MathematicsMediumIntegral Calculus369× since 2002

Let

f:R \to R

be a differentiable function having

f\left( 2 \right) = 6

f'\left( 2 \right) = \left( {{1 \over {48}}} \right)

. Then

\mathop {\lim }\limits_{x \to 2} \int\limits_6^{f\left( x \right)} {{{4{t^3}} \over {x - 2}}dt}

equals :