PLEASE SOLVE AND GIVE CORRECT ANSWER Q If f a + b - x = f - Maths - Integrals

Question

PLEASE SOLVE AND GIVE CORRECT ANSWER

Q     If   f   a   +   b   -
  x   =   f   ( x )   then   ∫
a b x   f   ( x )   dx   is   equal  
to 1   a - b 2 ∫ a b f ( x )   dx 2   a + b 2
∫ a b f ( x )   dx   3   0 4   none
  of   these

Rishabh Mittal · Accepted Answer

Dear Student,

Let I=∫ab x fx dx I= ∫ab a+b-x fa+b-x dx                Using property of definite integralI= ∫ab a+b-x fx dx I =∫ab a+b fx dx -∫ab x fx dx I=∫ab a+b fx dx -I2I= a+b∫ab fx dxI=a+b2 ∫ab fx dxCorrect option is 2

Regards

PLEASE SOLVE AND GIVE CORRECT ANSWER Q . If f a + b - x = f ( x ) then ∫ a b x f ( x ) dx is equal to 1 . a - b 2 ∫ a b f ( x ) dx 2 . a + b 2 ∫ a b f ( x ) dx 3 . 0 4 . none of these

PLEASE SOLVE AND GIVE CORRECT ANSWER

$Q . If f (a + b - x) = f (x) then \int_{a}^{b} x f (x) dx is equal to 1 . \frac{a - b}{2} \int_{a}^{b} f (x) dx 2 . (\frac{a + b}{2}) \int_{a}^{b} f (x) dx 3 . 0 4 . none of these$