//Zadanie 2, grupa A - METODA OBSZARÓW KOLOKACJI

clear

figure

n11=integrate ('1-x' , 'x' , 0, 1/3)
n12=integrate ('2*x-x^2' , 'x' , 0 ,1/3)
n13=integrate ('-x^3+3*x^2' , 'x' , 0 ,1/3)

n21=integrate ('1-x' , 'x' , 1/3, 2/3)
n22=integrate ('2*x-x^2' , 'x' , 1/3, 2/3)
n23=integrate ('-x^3+3*x^2' , 'x' , 1/3, 2/3)

n31=integrate ('1-x' , 'x' , 2/3, 1)
n32=integrate ('2*x-x^2' , 'x' , 2/3, 1)
n33=integrate ('-x^3+3*x^2' , 'x' , 2/3, 1)


q1=integrate ('x-1.5' , 'x' , 0 , 1/3)
q2=integrate ('x-1.5' , 'x' , 1/3 , 2/3)
q3=integrate ('x-1.5' , 'x' , 2/3 , 1)

A3=[n11 , n12, n13 ; n21 , n22 , n23 ; n31 , n32 , n33]
b3=[q1;q2;q3]
t3=linsolve (A3,b3)

x=0:0.1:1
    y3=1.5+t3(1,1)*x+t3(2,1)*x^2+t3(3,1)*x^3
plot (x,y3,'.-g')