curl --request POST \
  --url https://api.iotools.cloud/v1/tool/line-integral-calculator \
  --header 'Authorization: Bearer <token>' \
  --header 'Content-Type: application/json' \
  --data '
{
  "mode": "scalar",
  "dimension": "2d",
  "xt": "cos(t)",
  "yt": "sin(t)",
  "zt": "0",
  "t0": "0",
  "t1": "2*pi",
  "f": "x^2 + y^2",
  "p": "-y",
  "q": "x",
  "r": "0"
}
'

{
  "tool": "line-integral-calculator",
  "tool_version": "1.0.2",
  "outputs": {
    "scalarValue": "6.28319",
    "vectorValue": "",
    "arcLengthValue": "6.28319",
    "conservativeVerdict": "",
    "setup": "r(t) = (cos(t), sin(t)), t ∈ [0, 6.28319]; ∫_C f ds, f(x, y) = x^2 + y^2",
    "steps": "Curve: r(t) = (cos(t), sin(t)), t ∈ [0, 6.28319]\ndx/dt = -sin(t)\ndy/dt = cos(t)\nds/dt = sqrt((dx/dt)^2 + (dy/dt)^2)\nArc length = ∫ ds/dt dt = 6.28319\nf(x, y) = x^2 + y^2\n∫_C f ds = ∫ f(r(t)) · ds/dt dt = 6.28319\nMethod: composite Simpson's rule over t (1000 subdivisions); dx/dt, dy/dt computed via symbolic differentiation (mathjs derivative())."
  },
  "credits_used": 5,
  "credits_remaining": null
}