The function f(x) = ∫0xlog1 - x1 + xdx is
an even function
an odd function
a periodic function
None of these
A.
We know that, if f(t) is a odd function, then ∫0xftdt is an even function. Since the function f(x) = log1 - x1 + x is an odd function. ∫0xlog1 - x1 + xdx is an even function.