QJEEM19Ma6939: JEE Main 2019 Mathematics - Class 12 JEEM19Ma6939 Solution: Let f and g be continuous functions on [0, a] such that f(x) =…

Question

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Let f and g be continuous functions on [0, a] such that f(x) = f(a – x) and g(x) + g(a – x) = 4, then

\int_{0}^{a}

f(x) g(x) dx is equal to :

Accepted Answer

I = \int_{0}^{a} f (x) g (x) d x

I = \int_{0}^{a} f (a - x) g (a - x) d x

I = \int_{0}^{a} f (x) (4 - g (x) d x

I = 4 \int_{0}^{a} f (x) d x - I

\Rightarrow I = 2 \int_{0}^{a} f (x) d x

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