# Line Integral Calculator API

> For the complete documentation index, see [llms.txt](/llms.txt).

Evaluate scalar or vector line integrals along a parametric curve, with arc length and conservative-field check.

Use this endpoint to add the tool to your app, site, workflow, or agent without rebuilding formulas, validation, examples, and docs.

- Slug: `line-integral-calculator`
- Category: `math`
- Version: `2026-04-22`
- Credits per successful call: 1
- Starts on: free
- Max payload: 65536 bytes
- Privacy mode: `hash_only`
- Available on: free, starter, pro, business, scale
- Browser tool: https://miniwebtool.com/line-integral-calculator/

## Endpoint

`POST https://api.miniwebtool.com/v1/tools/line-integral-calculator/run`

## Request body

| Field | Type | Required | Description |
| --- | --- | --- | --- |
| `integral_type` | `str` | no | scalar | vector Choices: scalar, vector |
| `dimension` | `str` | no | 2 | 3 Choices: 2, 3 |
| `scalar_field` | `str` | no | f(x, y[, z]) for scalar integrals |
| `component_p` | `str` | no | i component for vector integrals |
| `component_q` | `str` | no | j component for vector integrals |
| `component_r` | `str` | no | k component for 3D vector integrals |
| `curve_x` | `str` | no | x(t) |
| `curve_y` | `str` | no | y(t) |
| `curve_z` | `str` | no | z(t) for 3D curves |
| `t_start` | `str` | no | parameter start |
| `t_end` | `str` | no | parameter end |

## Example request

```json
{
  "integral_type": "scalar",
  "dimension": "2",
  "scalar_field": "x + y",
  "curve_x": "cos(t)",
  "curve_y": "sin(t)",
  "t_start": "0",
  "t_end": "pi"
}
```

## cURL

```bash
curl -X POST https://api.miniwebtool.com/v1/tools/line-integral-calculator/run \
  -H 'Authorization: Bearer mwt_live_YOUR_KEY' \
  -H 'Content-Type: application/json' \
  -d '{"integral_type":"scalar","dimension":"2","scalar_field":"x + y","curve_x":"cos(t)","curve_y":"sin(t)","t_start":"0","t_end":"pi"}'
```

## Response envelope

```json
{
  "request_id": "01K...",
  "tool": "line-integral-calculator",
  "tool_version": "2026-04-22",
  "credits_used": 1,
  "result": {}
}
```

## Errors

Errors are RFC 7807 `application/problem+json`. Branch on `code`, not `title`.

## MCP

Agents can discover and call this tool through `https://api.miniwebtool.com/mcp` or `https://api.miniwebtool.com/v1/mcp` using MCP `tools/list` and `tools/call`.

## Frequently asked

### What does the Line Integral Calculator API do?

Evaluate scalar or vector line integrals along a parametric curve, with arc length and conservative-field check. Use it to add this utility without rebuilding formulas, validation, examples, and documentation.

### How much does one call cost?

1 credit per successful call. Failed calls do not bill.

### What parameters are required?

Required fields: (none). Full schema at `https://api.miniwebtool.com/v1/openapi.json`.

### Is this deterministic?

Yes. Same input, same output. Tool version: 2026-04-22.