fnint

Examples

The statementdiff(fnval(fnint(f),[a b]))provides the definite integral over the interval [a..b] of the function described byf.

Iffis in ppform, or in B-form with its last knot of sufficiently high multiplicity, then, up to rounding errors,fandfnder(fnint(f))are the same.

Iffis in ppform andfais the value of the function infat the left end of its basic interval, then, up to rounding errors,fandfnint(fnder(f),fa)are the same, unless the function described byfhas jump discontinuities.

Iffcontains the B-form off, andt₁is its leftmost knot, then, up to rounding errors,fnint(fnder(f))contains the B-form off–f(t₁). However, its leftmost knot will have lost one multiplicity (if it had multiplicity > 1 to begin with). Also, its rightmost knot will have full multiplicity even if the rightmost knot for the B-form offinfdoesn't.

这是一个例子last fact. The spline insp = spmak([0 0 1], 1)is, on its basic interval [0..1], the straight line that is 1 at 0 and 0 at 1. Now integrate its derivative:spdi = fnint(fnder(sp)). As you can check, the spline inspdihas the same basic interval, but, on that interval, it agrees with the straight line that is 0 at 0 and -1 at 1.

See the examples “Intro to B-form” and “Intro to ppform” for examples.