Question

Помогите решить задачу пожалуйста!

Answer 1

$a) y = 2x+3; y = 0, x=-1, x=2\\S = \int\limits^a_b {f(x)} \, dx\\S = \int\limits^2_{-1} {2x + 3} \, dx = (x^2 + 3x)|^2_{-1} = 4 + 6 - 1 + 3 = 12\\b) a) y = -3x; [2;4]\\V = \pi \int\limits^a_b {f^2(x)} \, dx\\V = \pi\int\limits^4_2 {9x^2} \, dx = 9\pi(\frac{x^3}{3}|^4_2) = 9\pi*\frac{56}3 = 168\pi\\b) y^2 = x +3, [-2; 1]\\y = \sqrt{x+3}\\V = \pi\int\limits^1_{-2} {x+3} \, dx = \pi (\frac{x^2}2 + 3x)|^1_{-2} = \frac{7\pi}2 + 4\pi = \frac{15\pi}2$