# Functions and Integration

Calculus Level 4

If $$f(x)$$ and $$\phi(x)$$ are continuous functions on the interval $$[0,6]$$ satisfying $$f(x)=f(6-x)$$ and $$\phi(x)+f(6-x)=5$$ and $$\displaystyle \int _{0}^{6} f(x)=3$$ then the value of

$$\large{\{\displaystyle \int ^{6}_{0} f(x) \phi(x) .dx\}}$$

where $$\{x\}$$ denotes fractional part of $$x$$

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