For the complete documentation index, see llms.txt.
Evaluate an iterated double integral over rectangular or variable-limit regions.
One POST adds Double Integral Calculator to your app, site, workflow, or agent — formula, validation, edge cases, and docs already handled.
prefer a UI? Open the Double Integral Calculator on miniwebtool.com →
POST https://api.miniwebtool.com/v1/tools/double-integral-calculator/run
| Field | Type | Req. |
|---|---|---|
function
integrand
|
str |
— |
outer_variable
single letter, integrated last
|
str |
— |
inner_variable
single letter, integrated first
|
str |
— |
outer_lower
constant lower limit
|
str |
— |
outer_upper
constant upper limit
|
str |
— |
inner_lower
may depend on the outer variable
|
str |
— |
inner_upper
may depend on the outer variable
|
str |
— |
65536 bytes.hash_only{
"request_id": "01K...",
"tool": "double-integral-calculator",
"tool_version": "2026-04-22",
"credits_used": 1,
"result": { ... }
}
1,000 free calls/mo · no card · key arrives by email
curl -X POST https://api.miniwebtool.com/v1/tools/double-integral-calculator/run \
-H 'Authorization: Bearer mwt_live_YOUR_KEY' \
-H 'Content-Type: application/json' \
-d '{"function":"x*y","outer_variable":"x","inner_variable":"y","outer_lower":"0","outer_upper":"1","inner_lower":"0","inner_upper":"1"}'
import requests
resp = requests.post(
'https://api.miniwebtool.com/v1/tools/double-integral-calculator/run',
headers={'Authorization': 'Bearer mwt_live_YOUR_KEY'},
json={'function': 'x*y', 'outer_variable': 'x', 'inner_variable': 'y', 'outer_lower': '0', 'outer_upper': '1', 'inner_lower': '0', 'inner_upper': '1'},
)
resp.raise_for_status()
data = resp.json()
print(data)
const resp = await fetch(
'https://api.miniwebtool.com/v1/tools/double-integral-calculator/run',
{
method: 'POST',
headers: {
'Authorization': 'Bearer mwt_live_YOUR_KEY',
'Content-Type': 'application/json',
},
body: JSON.stringify({"function":"x*y","outer_variable":"x","inner_variable":"y","outer_lower":"0","outer_upper":"1","inner_lower":"0","inner_upper":"1"}),
}
);
const data = await resp.json();
console.log(data);
<?php
$ch = curl_init('https://api.miniwebtool.com/v1/tools/double-integral-calculator/run');
curl_setopt_array($ch, [
CURLOPT_POST => true,
CURLOPT_RETURNTRANSFER => true,
CURLOPT_HTTPHEADER => [
'Authorization: Bearer mwt_live_YOUR_KEY',
'Content-Type: application/json',
],
CURLOPT_POSTFIELDS => json_encode([
'function' => 'x*y',
'outer_variable' => 'x',
'inner_variable' => 'y',
'outer_lower' => '0',
'outer_upper' => '1',
'inner_lower' => '0',
'inner_upper' => '1'
]),
]);
$resp = curl_exec($ch);
curl_close($ch);
print_r(json_decode($resp, true));
require 'net/http'
require 'json'
require 'uri'
uri = URI('https://api.miniwebtool.com/v1/tools/double-integral-calculator/run')
http = Net::HTTP.new(uri.host, uri.port)
http.use_ssl = (uri.scheme == 'https')
req = Net::HTTP::Post.new(uri)
req['Authorization'] = 'Bearer mwt_live_YOUR_KEY'
req['Content-Type'] = 'application/json'
req.body = {
'function' => 'x*y',
'outer_variable' => 'x',
'inner_variable' => 'y',
'outer_lower' => '0',
'outer_upper' => '1',
'inner_lower' => '0',
'inner_upper' => '1'
}.to_json
resp = http.request(req)
puts JSON.parse(resp.body).inspect
package main
import (
"bytes"
"encoding/json"
"fmt"
"io"
"net/http"
)
func main() {
body, _ := json.Marshal(map[string]interface{}{
"function": "x*y",
"outer_variable": "x",
"inner_variable": "y",
"outer_lower": "0",
"outer_upper": "1",
"inner_lower": "0",
"inner_upper": "1",
})
req, _ := http.NewRequest("POST", "https://api.miniwebtool.com/v1/tools/double-integral-calculator/run", bytes.NewReader(body))
req.Header.Set("Authorization", "Bearer mwt_live_YOUR_KEY")
req.Header.Set("Content-Type", "application/json")
resp, err := http.DefaultClient.Do(req)
if err != nil { panic(err) }
defer resp.Body.Close()
out, _ := io.ReadAll(resp.Body)
fmt.Println(string(out))
}
import java.net.URI;
import java.net.http.*;
var client = HttpClient.newHttpClient();
var req = HttpRequest.newBuilder()
.uri(URI.create("https://api.miniwebtool.com/v1/tools/double-integral-calculator/run"))
.header("Authorization", "Bearer mwt_live_YOUR_KEY")
.header("Content-Type", "application/json")
.POST(HttpRequest.BodyPublishers.ofString("{\"function\":\"x*y\",\"outer_variable\":\"x\",\"inner_variable\":\"y\",\"outer_lower\":\"0\",\"outer_upper\":\"1\",\"inner_lower\":\"0\",\"inner_upper\":\"1\"}"))
.build();
var resp = client.send(req, HttpResponse.BodyHandlers.ofString());
System.out.println(resp.body());
https://api.miniwebtool.com/v1/tools/double-integral-calculator/run
Authorization: Bearer <key> and Content-Type: application/json. Copy-paste snippets in 7 languages are under Code examples.
{request_id, tool, tool_version, credits_used, result}. The typed output lives in result.
Evaluate an iterated double integral over rectangular or variable-limit regions. Use it to add this utility without rebuilding formulas, validation, examples, and documentation.
1 credit per successful call. Failed calls (validation errors, 5xx) don't bill.
Required fields: (none). Full schema at /v1/openapi.json.
Yes — same input, same output, forever. Tool version 2026-04-22; output shape is stable within a major version.
Yes. Connect to https://api.miniwebtool.com/v1/mcp over the Model Context Protocol. The agent discovers `double-integral-calculator` with its JSON Schema automatically, so the model can plan while MiniWebtool handles the exact tool result.
JSON with a stable envelope: `{request_id, tool, tool_version, credits_used, result}`. Errors are RFC 7807 `application/problem+json`.
Every endpoint on this site is also exposed via the
Model Context Protocol at
https://api.miniwebtool.com/v1/mcp.
Claude, Cursor, and any MCP-capable agent can discover this tool
(double-integral-calculator)
and its JSON Schema automatically — no client codegen.
# List tools the agent can call
curl -s https://api.miniwebtool.com/v1/mcp \
-H 'Content-Type: application/json' \
-d '{"jsonrpc":"2.0","id":1,"method":"tools/list"}' \
| jq '.result.tools[] | select(.name=="double-integral-calculator")'