Question

50 баллов за решение!

Answer 1

$int _{frac{sqrt3}{3}}^{frac{2sqrt3}{3}}, frac{9dx}{sqrt{4-3x^2}}}=int frac{9dx}{sqrt3cdot sqrt{frac{4}{3}-x^2}}=3sqrt3cdot arcsinfrac{x}{frac{2}{sqrt3}}, |_{frac{sqrt3}{3}}^{frac{2sqrt3}{3}}=\\=3sqrt3(arcsin1-arcsinfrac{1}{2})=3sqrt3(frac{pi}{2}-frac{pi}{6})=3sqrt3cdot frac{pi}{3}=pi sqrt3$