Let f:[1,2] [0, ) be a continuous function such that f( x )=f[1- x ] for all x [-1,2] …
Mathematics · JEE Main · NTA Exams — Integral Calculus
Let \(f:[1,2] \rightarrow[0, \infty)\) be a continuous function such that \(f(\mathbf{x})=f[1-\mathbf{x}]\) for all \(x \in[-1,2]\). Let \(R_{1}=\int_{-1}^{2} x f(x) d x\) and \(R_{2}\) be the area of the region bounded by \(y=f(\mathbf{x}), \mathbf{x}=-1, \mathbf{x}=\mathbf{2}\) and the x -axis. Then,
- \(R_{1}=2 R_{2}\)
- \(R_{1}=3 R_{2}\)
- \(2 R_{1}=R_{2}\)
- \(3 R_{1}=R_{2}\)
Answer
(C) 2 R_ 1 =R_ 2
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