If ∫₀ˣ f(t) dt = x² + ∫ x ¹ t²f(t) dt then f ' (1/2) is -

Integral Calculus: JEE Main 2019 Mathematics question

JEE Main 2019 · 10 Jan, Evening shift · Q3303

JEE Main 201910 Jan, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

\int\limits_0^x \,

f(t) dt = x² +

\int\limits_x^1 \,

t²f(t) dt then f '

\left( {{1 \over 2}} \right)

is -

JEE Main 2019 · 10 Jan, Evening shift · Q3303

JEE Main 201910 Jan, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

\int\limits_0^x \,

f(t) dt = x² +

\int\limits_x^1 \,

t²f(t) dt then f '

\left( {{1 \over 2}} \right)

is -