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 'https://api.elysiatools.com/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 https://api.elysiatools.com/en/api/tools/numerical-integration-simpsonParameters
| 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": "https://api.elysiatools.com/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]