Let f :[-1,2] [0, ) be a continuous function such that f (x)= f (1-x), x [-1,2] Let R ₁= _ -1 ^2 x f (x) d x and R ₂ be the area of the region bounded by y= f (x), x=-1, x=2 and the X -axis, then R ₂ is

Step-by-step solution

Given that f (x)= f (1-x) and R ₁= _ -1 ^2 x f (x) d x aligned & R ₁= _ -1 ^2(1-x) f (1-x) d x & [ _ a ^ b f (x) d x= ₁^b f ( a + b -x) d x ] aligned R ₁= _ -1 ^2 f (x) d x- _ -1 ^2 x f (x) d x ... [ f(x)=f(1-x)] R ₁= _ -1 ^2 f (x) d x - R ₁ 2 R ₁= _ -1 ^2 f (x) d x Note that R ₂= _ -1 ^2 f (x) d x=2 R ₁