Question

Найти площадь фигуры, ограниченной параболой y=x^2+2 и прямой y=11​

Answer 1

$y=x^2+2\ \ ,\ \ y=11\\\\\\x^2+2=11\ \ ,\ \ x^2=9\ \x=\pm 3\\\\\\S=\int\limits^3_{-3}\, (11-x^2-2) \, dx=\int\limits^3_{-3}\, (9-x^2)\, dx=\Big(9x-\dfrac{x^3}{3}\Big)\Big|_{-3}^3=\\\\\\=27-\dfrac{27}{3}-\Big(-27+\dfrac{27}{3}\Big)=54-\dfrac{54}{3}=\dfrac{108}{3}=36$