JEE Main20253 Apr 2025Morning ShiftMathematicsIndefinite IntegrationActual

Let f(x)= x^3 3-x^2 d x . If 5 f( 2 )=-4 , then f(1) is equal to

Options

A- 2 2 5
B- 8 2 5
C- 4 2 5
D- 6 2 5

Correct answer

D. - 6 2 5

Step-by-step solution

aligned & Let 3-x^2=t^2 & +x d x=-t d t & f(x)= (3-t^2 ) t(-t d t)+c & = ( t ^4-3 t ^2 ) dt + c & = t ^5 5 - t ^3+ c & f ( x )= (3- x ^2 )^ 5 / 2 5 - (3- x ^2 )^ 3 / 2 + c & f ( 2 )= 1 5 -1+ c =- 4 5 aligned aligned & c =0 & f (1)= 2^ 5 / 2 5 -2^ 3 / 2 & =2^ 1 / 2 ( 4 5 -2 ) & f (1)- -6 2 5 aligned

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