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Let f:[-1,2] -> [0, infinity) be a continuous function satisfying f(x) = f(1 - x) for all x in [-1, 2]. Define R1 = integral from -1 to 2 of x*f(x) dx, and let R2 be the area of the region bounded by y = f(x), x = -1, x = 2 and the x-axis. Which relation holds?
- R1 = 2R2
- R1 = 3R2
- 2R1 = R2
- 3R1 = R2
Correct answer: 2R1 = R2
Solution
Substituting x -> 1 - x in R1 gives R1 = R2 - R1, hence 2R1 = R2.
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