Let f:[-2,3] [0, ) be a continuous function such that f(1-x)=f(x) for all x [-2,3] . If R ₁ is the numerical value of the area of the region bounded by y=f(x), x=-2, x=3 and the axis of x and R₂= _ -2 ^3 x f(x) d x , then :

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Correct answer: D. R ₁=2 R ₂

We have aligned R ₂ &= _ -2 ^3 x f(x) d x= _ -2 ^3(1-x) f(1-x) d x & [ U sing _a^b f(x) d x= _a^b f(a+b-x) d x ] R ₂ &= _ -2 ^3(1-x) f(x) d x R ₂+ R ₂ &= _ -2 ^3 x f(x) d x+ _ -2 ^3(1-x) f(x) d x 2 R ₂= R ₁ aligned

Let f:[-2,3] [0, ) be a continuous function such that f(1-x)=f(x) for all x [-2,3] . If R ₁ is the numerical value of the area of the region bounded by y=f(x), x=-2, x=3 and the axis of x and R₂= _ -2 ^3 x f(x) d x , then :

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