consider the quadrature formula on the interval [-1,1] using quadraturenodes x0= - alpha the formula also has precision 3. alpha for which the formula has precision 2. And finally show that for this alpah . Also show there is one value of W0 =w1 = 1 independent of Integrate f(x) dx wof(-alpha) + w1f(alpha) If this formula is to have precision 1 show 0 Solution Let w0 =-1 and w1=1 f(alpha) + f(-alpha) = -1 to 1 of integral f(x) dx i.e. 0 to 1 f(x) dx = f(alpha) Thus even for precision 2 and 3 this holds good. Hence proved..