**HP Prime: Area by Quadratic Splines**

**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.

Screen shot by HP Prime, labels I added using MS Paint (the old one) |

The number of points for QUADSUM must be odd.

**HP Prime Program QUADSUM**

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.

QUADSUM({0,1,2,3,4}, {2,1,2,6,4})
returns 12.6666666667

FYI: The polynomial described would be the
piecewise equation:

y = { x^2 -2x + 2 for 0 < x ≤
2, -3x^2 + 19x – 24 for 2 < x ≤ 4

Eddie

This blog is property of Edward
Shore, 2017

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