lab6

function numint

% y = x/(2*x+5)

a = -1; % нижний предел
b = 1; % верхний предел
h = 0.1; % шаг

X = [];
Y = [];

j = 1;
for i = a:h:b
  X(j) = i;
  Y(j) = X(j)/(2*X(j)+5);
  j += 1;
endfor
len = j-1;
disp(a:h:b);
disp("\n");

sum = 0;
for i = 2:len
  delta = abs(X(i)-X(i-1));
  sum += Y(i-1)*delta;
endfor
disp(" Методом левых прямоугольников:");
rect_left = sum

sum = 0;
for i = 2:len
  sum += Y(i)*delta;
endfor
disp("\n Методом правых прямоугольников:");
rect_right = sum

sum = 0;
for i = 2:len
  avgX = (X(i)+X(i-1))/2;
  sum += ((avgX/2)/(2*avgX+5))*delta;
endfor
disp("\n Методом средних прямоугольников:");
rect_middle = sum

sum = 0;
avgY = (Y(1)+Y(end))/2;
for i = 2:len-1
  sum += Y(i);
endfor
disp("\n Методом трапеций:");
trapeze_method = h*(avgY + sum);
trapeze_method

sumAVG = 0;
for i = 2:2:len-1
  sumAVG = (Y(i)+Y(i-1))/2;
endfor
disp("\n Методом Симпсона:");
simpson_method = h/6*(Y(1) + 4*sumAVG + 2*sum + Y(end));
simpson_method

end