Let f and g be continuous functions on


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 $\int_{0}^{a} f(x) g(x) d x$ is equal to :-

  1. $4 \int_{0}^{a} f(x) d x$

  2. $2 \int_{0}^{a} f(x) d x$

  3. $-3 \int_{0}^{a} f(x) d x$

  4. $\int_{0}^{a} f(x) d x$

Correct Option: , 2


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

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

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

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

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


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