If f(x) be a continuous function such th...

If `f(x)` be a continuous function such that `f(x)` does not vanish for all `x in R ,a n difint_(-1)^2f(x)dx=int_1^2f(x)dx ,t h e nf(x)i s` (A) an even function (B) an odd function (C) a periodic function (D) none of these

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Let f(x) be a continuous function in R such that f(x) does not vanish for all x in R . If int_1^5 f(x)dx=int_-1^5 f(x)dx , then in R, f(x) is (A) an even function (B) an odd function (C) a periodic function with period 5 (D) none of these

If f(x)={x^2sin(pix)/2,|x|<1x|x|,|x|geq1,t h e nf(x)i s an even function (b) an odd function a periodic function (d) none of these

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Let f(x) be a continuous function in R such that f(x)+f(y)=f(x+y) , then int_-2^2 f(x)dx= (A) 2int_0^2 f(x)dx (B) 0 (C) 2f(2) (D) none of these

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