Three Point Cubic (Posted on 2008-01-10)

      3         4
If  ∫c(x)dx = ∫c(x)dx, then what is c(3)?
    1          2

	Submitted by Brian Smith
Rating: 4.0000 (1 votes)
Solution:	(Hide)
For three points (x, a), (x+d, b), (x+2d, c), Simpson's Rule for numeric integration on the interval [x, x+2d] is exact for a cubic function. Integral(1,3)[c(x)]dx = (1/3)*(2 + 4*7 + c(3)) Integral(2,4)[c(x)]dx = (1/3)*(7 + 4*c(3) + 14) (1/3)*(2 + 4*7 + c(3)) = (1/3)*(7 + 4*c(3) + 14) 30 + c(3) = 21 + 4*c(3) c(3) = 3 Nikki has a more conventional approach here.

	Subject	Author	Date
	answer	K Sengupta	2008-02-06 06:21:35
	Little jewel!	Chesca Ciprian	2008-01-14 16:47:13
	Solution (I think)	nikki	2008-01-10 12:54:23