Let f, g and h be continuous functions on [$$0$$, a] such that $$f(x)=f(a$$−$$x)$$,$$g(x)=$$−$$g(a$$−$$x)$$ and $$3h(x)$$−$$4h(a$$−$$x)=5$$. Then ∫$$0a$$ $$f(x)g(x)h(x)dxis$$ equal to

Question

Let f, g and h be continuous functions on [$$0$$, a] such that $$f(x)=f(a$$−$$x)$$,$$g(x)=$$−$$g(a$$−$$x)$$ and $$3h(x)$$−$$4h(a$$−$$x)=5$$. Then ∫$$0a$$ $$f(x)g(x)h(x)dxis$$ equal to

Infinity Learn · Accepted Answer

$$I=$$∫$$0a$$ $$f(x)g(x)h(x)dx=$$∫$$0a$$ $$f(a$$−$$x)g(a$$−$$x)h(a$$−$$x)dx=$$∫$$0a$$ $$f(x){$$−$$g(x)}34h(x)$$−$$54dx74I=54$$∫$$0a$$ $$f(x)g(x)dx$$⇒$$I=57I1where$$ $$I1=$$∫$$0a$$ $$f(x)g(x)dx=$$∫$$0a$$ $$f(a$$−$$x)g(a$$−$$x)dx=$$∫$$0a$$ $$f(x)$$[−$$g(x)$$]$$dx=$$−$$I1$$⇒$$2I1=0$$⇒$$I1=0Thus$$, I $$=$$ $$0$$.

Let $f, g$ and h be continuous functions on [ $0, a$ ] such that $f (x) = f (a - x), g (x) = - g (a - x)$ and $3 h (x) - 4 h (a - x) = 5 . Then \int_{0}^{a} f (x) g (x) h (x) d x$
is equal to

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Let f, g and h be continuous functions on [0, a] such that f(x)=f(a−x),g(x)=−g(a−x) and 3h(x)−4h(a−x)=5. Then ∫0a f(x)g(x)h(x)dxis equal to

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Let $f, g$ and h be continuous functions on [ $0, a$ ] such that $f (x) = f (a - x), g (x) = - g (a - x)$ and $3 h (x) - 4 h (a - x) = 5 . Then \int_{0}^{a} f (x) g (x) h (x) d x$
is equal to