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Full Version: Area by Quadratic Splines
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Introduction

The program QUADSUM calculates the area under the curve described by the set of points (x_n, y_n). The points are connected, in groups of three, by quadratic splines. Thus, points (x1, y1), (x2, y2), and (x3, y3) are connected by a quadratic spline, (x3, y3), (x4, y4), (x5, y5) are connected by another quadratic spline, and so on.

The number of points for QUADSUM must be odd.

Code:
``` EXPORT QUADSUM(LX,LY) BEGIN // EWS 2017-12-10 // Area by connecting  // points using quadratic  // curves // number of points must be odd LOCAL A,S,T; // A=0 S:=SIZE(LX); IF FP(S/2)==0 THEN RETURN "Invalid: Number of points must be odd"; KILL; END; LOCAL T,M,MA,MB,MC; FOR T FROM 1 TO S-2 STEP 2 DO M:=CAS.LSQ([[1,LX(T),LX(T)^2], [1,LX(T+1),LX(T+1)^2], [1,LX(T+2),LX(T+2)^2]], [[LY(T)],[LY(T+1)],[LY(T+2)]]); MA:=M(3,1); MB:=M(2,1); MC:=M(1,1); A:=A+ (MA*LX(T+2)^3/3+MB*LX(T+2)^2/2+ MC*LX(T+2))- (MA*LX(T)^3/3+MB*LX(T)^2/2+ MC*LX(T)); END; RETURN A; END;```

Example

Find the area under the curve with these points connected by quadratic splines:
(0,2), (1,1), (2,2), (3,6), (4,4)

Note that the point (2,2) ends the first spline and starts the second.