Question

Вычислите определенный интеграл

Answer 1

$\huge \\ \int_{2}^{7}{4\over\sqrt{x}}\mathrm{dx}=4\int_{2}^{7}{1\over\sqrt{x}}\mathrm{dx}=4\cdot{x^{-{1\over2}+1}\over-{1\over2}+1}|_{2}^{7}=8\sqrt{x}|_{2}^{7}=8(\sqrt{7}-\sqrt{2})\\\\ \int_{2}^{7}{4\over\sqrt{x+2}}\mathrm{dx}=4\int_{2}^{7}{1\over\sqrt{x+2}}\mathrm{d(x+2)}=4\cdot{(x+2)^{-{1\over2}+1}\over-{1\over2}+1}|_{2}^{7}=8\sqrt{x+2}|_{2}^{7}=8(\sqrt{9}-\sqrt{4})=8$