I got a little bit confused on this integral, and the reason is because I got 2 different letters on the function, it tells me to differentiate.
$$F(x)=\int_{5x}^{6x+1}f(x+u)du$$
And I don't know what to do
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Do you know anything about $f(u)$? – Henry Apr 18 '19 at 22:48
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It is continuos. – Max Villegas Apr 18 '19 at 22:49
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It'll help if you write $F(x)=\int_{6x}^{7x+1}f(u)du$. – J.G. Apr 18 '19 at 23:03
1 Answers
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Hint: first off, fix $x$ for a moment and write $t = x+u$. Doing that change of variables will leave you with a different integral, with new limits
$$ F(x) = \int_{r(x)}^{s(x)}f(t)dt = \int^{s(x)}_0f(t)dt - \int_0^{r(x)}f(t)dt $$
and these terms can be computed via the theorem you know and a little extra work.
qualcuno
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Yes, in its simplest form. I'm substituting $t = x+u$ with $dt = \frac{d}{du}(x+u)du = du$. – qualcuno Apr 18 '19 at 22:55