Question

Помогите пожалуйста. 3-пример

Answer 1

$y=3-x^2\; ,\; \; y=x^2+1\\\\Tochki\; peresecheniya:\; \; 3-x^2=x^2+1\; ,\; \; 2x^2=2\; ,\; \; x^2=1\; ,\; \; x=\pm 1\\\\y(1)=y(-1)=2y=3-x^2\; \; \to \; \; x^2=3-y\\\\y=x^2+1\; \; \to \; \; x^2=y-1\\\\V=\pi \int\limits^a_b{x^2(y)}\, dy\\\\V=V_1+V_2=\pi \int\limits^2_1\, (y-1)\, dy+\pi \int\limits^3_2\, (3-y)\, dy=\\\\=\pi \cdot \frac{(y-1)^2}{2}\Big |_1^2+\pi \cdot \frac{-(3-y)^2}{2}\Big |_2^3=\frac{\pi}{2}\cdot \Big ((1-0)-(0-1)\Big )=\frac{\pi}{2}\cdot 2=\pi$