If f and g are continuous functions in [0, a] | vedclass

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(B) Let $I = \int_{0}^{a} f(x) g(x) dx$ ....$(1)$Using the property $\int_{0}^{a} h(x) dx = \int_{0}^{a} h(a - x) dx$,we get:$I = \int_{0}^{a} f(a - x

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

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(B) Let $I = \int_{0}^{a} f(x) g(x) dx$ ....$(1)$Using the property $\int_{0}^{a} h(x) dx = \int_{0}^{a} h(a - x) dx$,we get:$I = \int_{0}^{a} f(a - x) g(a - x) dx$Since $f(x) = f(a - x)$ and $g(a - x) = 4 - g(x)$,we have:$I = \int_{0}^{a} f(x) (4 - g(x)) dx$$I = 4 \int_{0}^{a} f(x) dx - \int_{0}^{a} f(x) g(x) dx$$I = 4 \int_{0}^{a} f(x) dx - I$Adding $I$ to both sides:$2I = 4 \int_{0}^{a} f(x) dx$$I = 2 \int_{0}^{a} f(x) dx$

If $f$ and $g$ are continuous functions in $[0, a]$ satisfying $f(x) = f(a - x)$ and $g(x) + g(a - x) = 4$,then $\int_{0}^{a} f(x) g(x) dx$ is equal to:

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