Why integration multiplies value in Google Sheets - Dashboard Impact

Dashboard Mode - Why integration multiplies value

Goal

Understand how integration in a spreadsheet multiplies value by summing small parts to get a total.

Sample Data

Time (hours)	Rate (units/hour)
0	2
1	3
2	4
3	5
4	6
5	7

Dashboard Components

• KPI Card: Total Units Produced
  Formula: =SUMPRODUCT((B2:B6+B3:B7)/2, A3:A7-A2:A6)
  Explanation: This formula calculates the total units by summing the average rate between each hour multiplied by the time interval (1 hour). Result: 22.5 units
• Line Chart: Rate over Time
  Shows how the rate changes each hour from 2 to 7 units/hour.
• Table: Incremental Units Produced per Interval
  Formula in C3: =((B3+B2)/2)*(A3-A2) copied down to C7
  Shows units produced each hour interval by multiplying average rate by time difference.

Dashboard Layout

+----------------------+-------------------+
|      KPI Card        |    Line Chart     |
|  Total Units: 22.5   |  Rate vs Time     |
+----------------------+-------------------+
|          Table: Incremental Units Produced          |
+-----------------------------------------------------+

Interactivity

User can change the rates in column B. The KPI card and table update automatically to show new total units and incremental units. The line chart updates to reflect the new rate changes over time.

Self Check

If you change the rate at hour 3 from 5 to 10, which components update and what happens to the total units?

Answer: The KPI card, line chart, and incremental units table all update. The total units increase because the rate is higher at hour 3, increasing the sum of all intervals.

Key Result

A dashboard showing how integration sums small rate intervals over time to calculate total units produced.