A) \[\int_{-2}^{2}{f(x)}dx=\int_{0}^{2}{[f(x)-f(-x)]}\,dx\]
B) \[\int_{-3}^{5}{2f(x)}dx=\int_{-6}^{10}{f(x-1)}\,dx\]
C) \[\int_{-3}^{5}{f(x)\,}dx=\int_{-4}^{4}{f(x-1)}\,dx\]
D) \[\int_{-3}^{5}{f(x)\,}dx=\int_{-2}^{6}{f(x-1)}\,dx\]
E) \[\int_{-3}^{5}{f(x)\,}dx=\int_{-6}^{10}{f\left( \frac{x}{2} \right)}\,dx\]
Correct Answer: B
Solution :
\[\because \]\[f(x)\]is a continuous function. Let us consider\[f(x)=x\] \[\therefore \] \[\int_{-3}^{5}{2x}\,dx=16\] and \[\int_{-6}^{10}{(x-1)}\,dx=16\] \[\therefore \] \[\int_{-3}^{5}{2f\,(x)}\,dx=\int_{-6}^{10}{f(x-1)}\,dx\]
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