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Questions Asked in Previous 10 Years' Exams
Let \( f:[-1,2] \rightarrow[0, \infty) \) be a continuous function such that \( f(x)=f(1-x), \forall x \in[-1,2] \) If \( R_{1}=\int_{-1}^{2} x f(x) d x \) and \( R_{2} \) are the area of the region bounded by \( y=f(x) \), \( x=-1, x=2 \) and the \( X \)-axis. Then,
[Single Correct Optlon 2011]
(a) \( R_{1}=2 R_{2} \)
(b) \( R_{1}=3 R_{2} \)
(c) \( 2 R_{1}=R_{2} \)
(d) \( 3 R_{1}=R_{2} \)
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