The value of f( l ) , given the equation ₀^ x^2 x f(t) d t=x^5-x^3 is

Step-by-step solution

₀^ x^2 x f(t) d t=x^5-x^3 Differentiate w.r.t. x on both sides, aligned x^2 f (x^2 ) d d x x^2-0 & =5 x^4-3 x^2 x^2 f (x^2 )(2 x) & =5 x^4-3 x^2 aligned 2 x^3 f (x^2 )=5 x^4-3 x^2 Put x=1 2 1 f(1)=5(1)-3(1) f(1)=1 Hence, option (4) is correct.