Trapezoidal rule: T_n against the exact integral

Year 12 Mathematics Advanced · T_n = h/2 [y₀ + 2(y₁ + … + y_n−1) + y_n] · h = (b − a)/n · n strips need n + 1 values

Curve

curve trapezoids chord above curve chord below curve

n strips 4

4 strips → 5 function values (y₀ to y₄), width h = 0.5

T_n (trapezoidal) –

exact ∫_a^b f(x) dx –

closed form –

error T_n − exact –

relative –

End values carry coefficient 1; every interior value is an edge shared by two trapezoids, so it carries 2.

The exact value, the error and the verdict stay masked until you commit. Look at the shading first: is the chord above or below the curve?