Question

x
$x \sqrt{1 + y ^{2} } dx + y \sqrt{1 - x ^{2} } dy$
помогите решить​

Answer 1

Ответ:

$x\, \sqrt{1+y^2}\, dx+y\, \sqrt{1-x^2}\, dy=0\\\\\\x\, \sqrt{1+y^2}\, dx=-y\, \sqrt{1-x^2}\, dy\\\\\int \dfrac{x\, dx}{\sqrt{1-x^2}}=-\int \dfrac{y\, dy}{\sqrt{1+y^2}}\\\\\\-\sqrt{1-x^2}=-\sqrt{1+y^2}+C\\\\\sqrt{1+y^2}=\sqrt{1-x^2}+C$