Question 46

Let $$f:[-1, 2] \rightarrow [0, \infty)$$ be a continuous function such that $$f(x) = f(1 - x)$$ for all $$x \in [-1, 2]$$. Let $$R_1 = \int_{-1}^{2} x f(x)dx$$ and $$R_2$$ be the area of the region bounded by y = f(x), x = -1, x = 2, and the x-axis. Then

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