Question

Let f (x) = 7tan⁸ x + 7tan⁶ x - 3tan⁴ x - 3tan² x for all x ∈ \((-\frac{\pi}{2},\frac{\pi}{2})\). Then the correct expression(s) is(are)

 (A) \(\int\limits_0^{\pi /4}\) xf (x) dx = 1/12

(B) \(\int\limits_0^{\pi /4}\) f(x)dx = 0

(C) \(\int\limits_0^{\pi /4}\) xf (x)dx = 1/6

(D) \(\int\limits_0^{\pi /4}\)f(x)dx = 1

Answer 1

(A) \(\int\limits_0^{\pi /4}\) xf (x) dx = 1/12

(B) \(\int\limits_0^{\pi /4}\) f(x)dx = 0