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darboux_sum

Compute the Darboux sum for a function over a specified interval by defining the function, variable, limits, and subintervals. Choose between upper or lower sums to approximate the integral accurately.

Instructions

Calculate the Darboux sum of a function

Input Schema

Name	Required	Description	Default
`a`	Yes	Lower limit of integration
`b`	Yes	Upper limit of integration
`expression`	Yes	Function to integrate
`n`	Yes	Number of subintervals
`type`	No	Type: upper or lower Darboux sum	upper
`variable`	Yes	Variable of integration

Input Schema (JSON Schema)

{
  "$schema": "http://json-schema.org/draft-07/schema#",
  "additionalProperties": true,
  "properties": {
    "a": {
      "description": "Lower limit of integration",
      "type": "number"
    },
    "b": {
      "description": "Upper limit of integration",
      "type": "number"
    },
    "expression": {
      "description": "Function to integrate",
      "type": "string"
    },
    "n": {
      "description": "Number of subintervals",
      "type": "number"
    },
    "type": {
      "default": "upper",
      "description": "Type: upper or lower Darboux sum",
      "enum": [
        "upper",
        "lower"
      ],
      "type": "string"
    },
    "variable": {
      "description": "Variable of integration",
      "type": "string"
    }
  },
  "required": [
    "expression",
    "variable",
    "a",
    "b",
    "n"
  ],
  "type": "object"
}

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