darboux_sum
Compute the upper or lower Darboux sum for a function over a specified interval, dividing it into subintervals to approximate the integral.
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"
}