Practice question · Numerical answer
Measured values of a function at x = 0, 1, 2, 3 are 1, 3, 5 and 9. Apply the trapezoidal rule with step size 1 to estimate the integral from 0 to 3.
Hints
- Each interior height counts once; the two end heights count half each.
- Compute 0.5 + 3 + 5 + 4.5.
Show the answer
13
Why
The estimate is 1/2 + 3 + 5 + 9/2 = 13. The halved end weights are the whole content of the trapezoidal rule, and giving every height full weight instead is the standard slip, it would have given 18 here.
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