Question

If f(2 − x) = f(2 + x) and f(4 − x) = f(4 + x) for all x and f(x) is a function for which \(\int\limits_0^2\)f(x)dx = 5, then \(\int\limits_0^{50}\)​ f(x) dx is equal to

(a) 125 

(b) \(\int\limits_{-4}^{46}\) f(x) dx

(c) \(\int\limits_1^{51}\) f(x) dx

(d) \(\int\limits_2^{52}\) f(x) dx

Answer 1

Correct options are (A), (B) & (D)

(in second integral replacing x by x+48 and then using f(x) = f(x + 48))

Now checking option B

Now checking option C

Now checking option D