# Calculus Integration question

### Calculus Integration question

How do you do this?
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### Re: Calculus Integration question

I am thinking that I saw this on another board and the answer was given there is no one answer- you can choose different f that match the two conditions but give different answers for the question.

For example, if f(x)= 2 for all x then $$\int_0^3 f(x)= 6$$ and $$\int_3^5 f(x)dx= 4$$ as required and, in this case, $$\int_0^5 f(3+ 2f(x))dx= \int_0^5 2 dx= 10$$.

But if f(x)= (4/3)x for $$0\le x\le 3$$ and $$f(x)= (1/2)x$$ for $$3\le x$$ then is is still true that $$\int_0^3 f(x)dx 6$$ and that $$\int_3^5 f(x)dx= 4$$. But now $$\int_0^5 f(3+ 2f(x)) dx= 65/3$$.

HallsofIvy

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