определенный интеграл!!! нижний интеграл 1 верхний 4....(sqrt(x)) (3-(7/x))dx. Created by Dj0Sergey. algebra-ru

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определенный интеграл!!!
нижний интеграл 1 верхний 4....(sqrt(x)) (3-(7/x))dx

Gerren $\int\limits^4_1 \, \sqrt{x}\cdot (3-\frac{7}{x}) \, dx = \int\limits^4_1\, {(3\sqrt{x}-\frac{7}{\sqrt{x}}) \, dx =( \frac{3x^{3/2}}{3/2} -7\cdot 2\sqrt{x})\Big |_1^4=$

$=(2\sqrt{x^3}-14\sqrt{x})\Big |_1^4=(2\sqrt{4^3}-14\sqrt4)-(2-14)=\\\\=2\cdot 2\cdot 4-14\cdot 2-(-12)=16-28+12=0$

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Verified answer

∫1,4(√x(3-7/x)dx=∫1,4(3√x-7x^(-1/2))dx=|4,1(2x-14)√x=(2*4-14)√4-(2-14)=12-12=0

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