2.5.3—Trapezium rule

With equal spacing h and ordinates y₀,…,yₙ, the trapezium estimate is h/2[y₀+yₙ+2(y₁+…+yₙ₋₁)]. It approximates the definite integral by straight chords.

Use n subintervals and h=(b−a)/n. For a curve that is concave up, the chord estimate lies above or below according to the curvature, so compare with an exact value when available.

Using h=0.5 with ordinates at x=0,0.5,1 gives area ≈0.25[y₀+2y₁+y₂].

The number of ordinates is n+1, not n, and the endpoint weights are 1 rather than 2.