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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1
If f  (x)=f  (a−x)  and  g(x)  +  g(a−x)=2f\,\,\left( x \right) = f\,\,\left( {a - x} \right)\,\,\mathrm{and}\,\,\mathrm{g}\left( x \right)\,\, + \,\,\mathrm{g}\left( {a - x} \right) = 2,then the value of ∫0a  f(x)  g  (x)  dx  is\int \nolimits_0^a \,\,f\left( x \right)\,\,\mathrm{g}\,\,\left( x \right)\,\,dx\,\,\mathrm{is} is
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Correct option: A
∫0a  f  (x)  dx\int \nolimits_0^a \,\,f\,\,\left( x \right)\,\,dx
Option A (∫0a  f  (x)  dx\int \nolimits_0^a \,\,f\,\,\left( x \right)\,\,dx) is correct because by substituting x with a-x and using the given properties, the integral simplifies to this form.

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