[tex] \int\limits^2_{-3} \, dx / \ sqrt{7-3x} [/tex]. Created by zla1747. algebra-ru

tex]...

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[tex] \int\limits^2_{-3} \, dx / \
sqrt{7-3x} [/tex]

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$\int _{-3}^2\, \frac{dx}{\sqrt{7-3x}}=[\, d(7-3x)=-3\, dx\, ]=-\frac{1}
{3}\int_{-3}^2\frac{d(7-3x)}{\sqrt{7-3x}}=\\\\=-\frac{1}{3}\cdot 2\sqrt{7-3x}\, |_{-3}^2=-\frac{2}{3}(\sqrt{7-6}-\sqrt{7+9})=-\frac{2}{3}(1-4)=2$

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