Let x2 be the given mid-point and h>0. Let x = 22 h, x3 = x2...

 

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Let x2 be the given mid-point and h>0. Let x = 22 h, x3 = x2 +h. (a) (10 points) Find the constants c1, c2, and c3 such that the quadrature formula [** f(x)dx = c1 f (x1) + c2f(x2) + c3f(x3) 1 has the highest possible degree of precision. (b) (5 points) Show that the degree of precision of the formula from(a) is 3. (You only need to check that the formula is exact for f(x) = x, but not exact for f(x) = x4) Let x2 be the given mid-point and h>0. Let x = 22 h, x3 = x2 +h. (a) (10 points) Find the constants c1, c2, and c3 such that the quadrature formula [** f(x)dx = c1 f (x1) + c2f(x2) + c3f(x3) 1 has the highest possible degree of precision. (b) (5 points) Show that the degree of precision of the formula from(a) is 3. (You only need to check that the formula is exact for f(x) = x, but not exact for f(x) = x4)