MCQ
$f(x) = f(2 - x),$ તો $\int_{\,0.5}^{\,1.5} {\,xf(x)\,dx} =$
- A$\int_{\,0}^{\,1} {\,f(x)\,dx} $
- ✓$\int_{\,0.5}^{\,1.5} {\,f(x)\,dx} $
- C$2\int_{\,0.5}^{\,1.5} {\,f(x)\,dx} $
- D$0$
$\left[ \because \int_{a}^{b}{f(x)dx=\int_{a}^{b}{f(a+b-x)dx}} \right]$
$ = \int_{0.5}^{1.5} {(2 - x)f(x)\,dx} = 2\int_{0.5}^{1.5} {f(x)\,dx - I} $
==>$I = \int_{0.5}^{1.5} {f(x)\,dx} $.
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