kokoszzm
2022-06-24
Answered

Calculate ${\int}_{4}^{7}f(x)f(2x)dx$

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g2joey15

Answered 2022-06-25
Author has **21** answers

You are absolutely correct. When $x\in (4,7)$, you have that $2x\in (8,14)$, which means that $f(x)f(2x)=0$ for $x\in (4,7)$. This implies that ${\int}_{4}^{7}f(x)f(2x)\phantom{\rule{thinmathspace}{0ex}}dx=0$

April Bush

Answered 2022-06-26
Author has **6** answers

First of all you have to calculate $f(2x)$

$f(2x)=\{\begin{array}{ll}2x& 4\le 2x<7\\ 0& otherwise\end{array}$

$f(2x)=\{\begin{array}{ll}2x& 2\le x<\frac{7}{2}\\ 0& otherwise\end{array}$

${\int}_{4}^{7}f(x)f(2x)dx={\int}_{4}^{7}x\times 0.dx={\int}_{4}^{7}0.dx=0$

$f(2x)=\{\begin{array}{ll}2x& 4\le 2x<7\\ 0& otherwise\end{array}$

$f(2x)=\{\begin{array}{ll}2x& 2\le x<\frac{7}{2}\\ 0& otherwise\end{array}$

${\int}_{4}^{7}f(x)f(2x)dx={\int}_{4}^{7}x\times 0.dx={\int}_{4}^{7}0.dx=0$

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