Most Important Selected Qs for JEE AdvancedMathematicsIndefinite Integration

The value of f^ (x) F(x) d x- f(x) F^ (x) d x is equal to

Options

Af(x) F(x)-f^ (x) F^ (x)+c
Bf^ (x) F(x)-f(x) F^ (x)+c
Cf(x) F^ (x)-F(x) f^ (x)+c
Df^ (x) F^ (x)-F^ (x) f^ (x)+c

Correct answer

B. f^ (x) F(x)-f(x) F^ (x)+c

Step-by-step solution

aligned & I= (f^ (x) F(x)-f(x) F^ (x) ) d x= (f^ (x) F(x)+f^ (x) F^ (x) )- (f(x) F^ (x)+f^ (x) F^ (x) ) d x & = d (f^ (x) F(x)-f(x) F^ (x) )=f^ (x) F(x)-f(x) F^ (x)+c aligned

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