Let f : [–1, 2] → [0, ∞ ) be a continuous function such that f ( x ) = f (1 – x ) for all…
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
Let f : [–1, 2] → [0, ∞) be a continuous function such that f(x) = f(1 – x) for all x ∈ [–1, 2]. \(\text { Let } R_{1}=\int_{-1}^{2} x f(x) d x,\) and R2 be the area of the region bounded by y = f(x),
x = –1, x = 2, and the x-axis. Then
x = –1, x = 2, and the x-axis. Then
- R1 = 2R2
- R1 = 3R2
- 2R1 = R2
- 3R1 = R2
Answer
(C) 2 R 1 = R 2
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