Area = Displacement

Velocity is constant. The area under the velocity curve tells us how far the car moved.

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0m {{ s1_v * 5 }}m
Drag to drive
Displacement =

Net Displacement

When velocity drops below zero, the car goes backwards! The integral calculates net displacement.

Tap Area 1
Forward: +{{ s2_area1Val }}m
Tap Area 2
Backward: {{ s2_area2Val }}m
Net Displacement = {{ s2_area1Val }} + {{ s2_area2Val }} = {{ s2_area1Val + s2_area2Val }}m Find both areas to calculate total displacement

Total Distance Traveled

To find total distance (like an odometer), we integrate speed . Negative velocity becomes positive!

Drag vertex up to flip curve
Total Distance = {{ s3_area1Val }} + {{ Math.abs(s3_area2Val) }} = {{ s3_area1Val + Math.abs(s3_area2Val) }}m

Average Value of a Function

The average value is the height of a rectangle that has the same area as the region under the curve.

Curve Area
{{ s4_curveArea.toFixed(1) }}
Rectangle Area
{{ s4_rectArea.toFixed(1) }}
Drag line to level areas Perfect! Avg Value = {{ s4_avgValue.toFixed(2) }}
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Mastered!

You've unlocked the secrets of integration in motion: