Mathematics · University
Composite trapezoid approximation
This is an approximation to the integral. For a convex quadratic it overestimates the exact area.
Method and conditions
This is an approximation to the integral. For a convex quadratic it overestimates the exact area.
Tₙ = h[f₀/2 + Σfᵢ + fₙ/2]
Worked examples
Use the composite trapezoidal rule with 9 equal panels for the integral of 9x² from 0 to 11. Round the final result to 4 decimal places if needed.
Panel width is 11/9. Sum the interior values with weight 1 and the endpoints with weight 1/2, then multiply by the panel width.
4017.6481
Use the composite trapezoidal rule with 12 equal panels for the integral of 3x² from 0 to 2. Round the final result to 4 decimal places if needed.
Panel width is 2/12. Sum the interior values with weight 1 and the endpoints with weight 1/2, then multiply by the panel width.
8.0278
Try it
Use the composite trapezoidal rule with 11 equal panels for the integral of 3x² from 0 to 12. Round the final result to 4 decimal places if needed.
Use the composite trapezoidal rule with 3 equal panels for the integral of 7x² from 0 to 9. Round the final result to 4 decimal places if needed.
Check your work
Answers and marking notes
- 1735.1405
Panel width is 12/11. Sum the interior values with weight 1 and the endpoints with weight 1/2, then multiply by the panel width.
- 1795.5
Panel width is 9/3. Sum the interior values with weight 1 and the endpoints with weight 1/2, then multiply by the panel width.
Further reading and review references
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