If ∫ cos xdx sin ³x (1 + sin ⁶x)^(2/3) = f(x)(1 + sin ⁶x)^(1/λ) + c where c is a constant of integration, then λ f((π)/3) is equal to

Integral Calculus: JEE Main 2020 Mathematics question

JEE Main 2020 · 8 Jan, Morning shift · Q4026

JEE Main 20208 Jan, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

\int {{{\cos xdx} \over {{{\sin }^3}x{{\left( {1 + {{\sin }^6}x} \right)}^{2/3}}}}} = f\left( x \right){\left( {1 + {{\sin }^6}x} \right)^{1/\lambda }} + c

where c is a constant of integration, then

\lambda f\left( {{\pi \over 3}} \right)

is equal to

JEE Main 2020 Integral Calculus Question with Solution (8 Jan Morning shift, Q4026) | JEE Arc

JEE Main 2020 · 8 Jan, Morning shift · Q4026

JEE Main 20208 Jan, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

\int {{{\cos xdx} \over {{{\sin }^3}x{{\left( {1 + {{\sin }^6}x} \right)}^{2/3}}}}} = f\left( x \right){\left( {1 + {{\sin }^6}x} \right)^{1/\lambda }} + c

where c is a constant of integration, then

\lambda f\left( {{\pi \over 3}} \right)

is equal to