Ответ:

Объяснение:

1) просто інтегрування

F(x) = x^(5/2)/(5/2) + C

F(b) - F(a) = F(3) - F(1) = 3^(5/2)/(5/2) - 1^(5/2)/(5/2) = 2/5 * (3^(5/2) - 1) ~= 5.8353829072

2) методів середніх прямокутників

x_i = a + i*h = 1 + 0.2*i

h = (b-a)/n = 0.2

S = f(1.1)*0.2 + f(1.3)*0.2 + f(1.5)*0.2 + f(1.7)*0.2 + f(1.9)*0.2 + f(2.1)*0.2 + f(2.3)*0.2 + f(2.5)*0.2 + f(2.7)*0.2 + f(2.9)*0.2 ~= 1.153689732987167*0.2 + 1.4822280526288794*0.2 + 1.8371173070873836*0.2 + 2.216528817768901*0.2 + 2.618969262897142*0.2 + 3.043189116699782*0.2 + 3.488122704263713*0.2 + 3.952847075210474*0.2 + 4.436552715791846*0.2 + 4.938522046118657*0.2 ~= 5.83355336629079

Похибка

f''(x) = 3/4 * x^(-1/2)

f''(1) = 0.75 - max

f''(3) = 0.43

E(f) = f''_max * (b-a)^3 / (24 * n^2) = 3/4 * (3-1)^3 / (24 * 10^2) = 0.0025

3) Метод Сімпсона

S = (b-a)/6 * (f(a) + 4*f((a+b)/2) + f(b)) = (3-1)/6 * (f(1) + 4*f(2) + f(3)) = (3-1)/6 * (1^(3/2) + 4*2^(3/2) + 3^(3/2)) = 5.8366203072

Похибка

f''''(x) = 9/16 * x^(-5/2)

f''''(1) = 9/16 * 1^(-5/2) = 0.5625 - max

f''''(2) = 9/16 * 3^(-5/2) = 0.0360843918

E(f) = (b - a)^5 / 2880 * f''''_max = (3 - 1)^5 / 2880 * 0.5625 = 0.00625