DOCS-14703 derivative and integral updates

Author: jason-price-mongodb

source/includes/extracts-agg-operators.yaml

@@ -1188,8 +1188,8 @@ content: |
 
       * - :group:`$derivative`
 
-        - Returns the mathematical derivative of the numeric
-          :ref:`expression <aggregation-expressions>`. 
+        - Returns the average rate of change within the specified
+          :ref:`window <setWindowFields-window>`.
 
           .. versionadded:: 5.0
 
@@ -1221,8 +1221,7 @@ content: |
 
       * - :group:`$integral`
 
-        - Returns the mathematical integral of the numeric
-          :ref:`expression <aggregation-expressions>`.
+        - Returns the approximation of the area under a curve.
 
           .. versionadded:: 5.0
 

source/reference/operator/aggregation.txt

@@ -416,8 +416,8 @@ Alphabetical Listing of Expression Operators
 
    * - :group:`$derivative`
 
-     - Returns the mathematical derivative for the numeric
-       :ref:`expression <aggregation-expressions>`.
+     - Returns the average rate of change within the specified
+       :ref:`window <setWindowFields-window>`.
 
        .. versionadded:: 5.0
 
@@ -560,8 +560,7 @@ Alphabetical Listing of Expression Operators
 
    * - :group:`$integral`
 
-     - Returns the mathematical integral for the numeric
-       :ref:`expression <aggregation-expressions>`.
+     - Returns the approximation of the area under a curve.
 
        .. versionadded:: 5.0
 

source/reference/operator/aggregation/derivative.txt

@@ -17,8 +17,8 @@ Definition
 
 .. group:: $derivative
 
-Returns the mathematical derivative value, which is calculated using
-the:
+Returns the average rate of change within the specified :ref:`window
+<setWindowFields-window>`, which is calculated using the:
 
 - First and last documents in the :pipeline:`$setWindowFields` stage
   :ref:`window <setWindowFields-window>`.

source/reference/operator/aggregation/integral.txt

@@ -17,12 +17,12 @@ Definition
 
 .. group:: $integral
 
-Returns an approximation for the mathematical integral value, which is
-calculated using the trapezoidal rule with each set of adjacent
-documents forming a trapezoid using the:
+Returns the approximation of the area under a curve, which is
+calculated using the trapezoidal rule where each set of adjacent
+documents form a trapezoid using the:
 
 - :ref:`sortBy <setWindowFields-sortBy>` field values in the
-  :pipeline:`$setWindowFields` stage for the x axis values.
+  :pipeline:`$setWindowFields` stage for the integration intervals.
 
 - :ref:`input <integral-input>` field :ref:`expression
   <aggregation-expressions>` result values in :group:`$integral` for the