Question

∫_0^1▒xdx/√(1-x^2 ) решить интеграл

Answer 1

$intlimits^1_0 {frac{xdx}{sqrt{1-x^2}}}\ t = 1-x^2\ dt=-2xdx\ t(0) = 1\ t(1) = 0\ intlimits^0_1 {frac{-(1/2)dt}{sqrt{t}}}=-1/2(2sqrt{t}})|limits^0_1 = -sqrt(t)|limits^0_1 =1$