Math & Numbers

Trapezoidal Rule Integrator (∫f(x)dx)

Composite trapezoidal rule for ∫f(x)dx: node table, integral estimate, optional exact value and O(h²) error report.

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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-trapezoid' \
  -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-trapezoid

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	h = (b − a)/n. More subintervals → smaller error, O(h²) globally.
exactF	text	No	Exact antiderivative in x; the tool reports F(b) − F(a) and the absolute error. Leave empty to skip.

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-trapezoid": {
      "name": "numerical-integration-trapezoid",
      "description": "Composite trapezoidal rule for ∫f(x)dx: node table, integral estimate, optional exact value and O(h²) error report.",
      "baseUrl": "http://127.0.0.1:3003/mcp/sse?toolId=numerical-integration-trapezoid",
      "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-trapezoid",
    "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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