Math & Numbers

Simpson's Rule Integrator (∫f(x)dx)

Composite Simpson's 1/3 rule for ∫f(x)dx (even n): node table with weights, integral estimate, optional exact value, O(h⁴) accuracy.

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Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'http://127.0.0.1:3003/en/api/tools/numerical-integration-simpson' \
  -H 'Content-Type: application/json' \
  -d '{"fx":"x^2","a":0,"b":1,"n":4,"exactF":"x^3/3","decimalPlaces":6}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST http://127.0.0.1:3003/en/api/tools/numerical-integration-simpson

Parameters

Name	Type	Required	Description
fx	text	Yes	Integrand in x (functions: sin, cos, exp, ln, sqrt, …).
a	number	Yes	—
b	number	Yes	May be less than a (the integral flips sign, as in calculus).
n	number	Yes	Must be even. h = (b − a)/n; global error is O(h⁴) — halving h divides the error by ~16.
exactF	text	No

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-numerical-integration-simpson": {
      "name": "numerical-integration-simpson",
      "description": "Composite Simpson's 1/3 rule for ∫f(x)dx (even n): node table with weights, integral estimate, optional exact value, O(h⁴) accuracy.",
      "baseUrl": "http://127.0.0.1:3003/mcp/sse?toolId=numerical-integration-simpson",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "numerical-integration-simpson",
    "arguments": {
  "fx": "x^2",
  "a": 0,
  "b": 1,
  "n": 4,
  "exactF": "x^3/3",
  "decimalPlaces": 6
}
  }
}

Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

Questions or issues? Contact [email protected]

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