LimitsHard

Question

Let f : [-1, 2] → [0, ∞) be a continuous function such that f(x) = f (1 - x) for all x ε [-1, 2]. Let R4 f(x)dx, and R2 be the area of the region bounded by y = f(x), x = -1, x = 2, and the x-axis. Then

Options

A.R1 = 2R2
B.R1 = 3R2
C.2R1 = R2
D.3R1 = R2

Solution

R1 = f(x)dx = (2 - 1 - x)f(2 - 1 - x)dx
= (1 - x)f(1 - x) dx = (1 - x)f(x)dx
Hence 2R1 = f(x)dx = R2

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