# Calculate <msubsup> &#x222B;<!-- ∫ --> <mrow class="MJX-TeXAtom-ORD"> 4 </mrow>

Calculate ${\int }_{4}^{7}f\left(x\right)f\left(2x\right)dx$
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g2joey15
You are absolutely correct. When $x\in \left(4,7\right)$, you have that $2x\in \left(8,14\right)$, which means that $f\left(x\right)f\left(2x\right)=0$ for $x\in \left(4,7\right)$. This implies that ${\int }_{4}^{7}f\left(x\right)f\left(2x\right)\phantom{\rule{thinmathspace}{0ex}}dx=0$
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April Bush
First of all you have to calculate $f\left(2x\right)$
$f\left(2x\right)=\left\{\begin{array}{ll}2x& 4\le 2x<7\\ 0& otherwise\end{array}$
$f\left(2x\right)=\left\{\begin{array}{ll}2x& 2\le x<\frac{7}{2}\\ 0& otherwise\end{array}$
${\int }_{4}^{7}f\left(x\right)f\left(2x\right)dx={\int }_{4}^{7}x×0.dx={\int }_{4}^{7}0.dx=0$