Signed Area

Above counts plus, below counts minus

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• The definite integral is signed area: above the axis is positive, below is negative.
• The integral of velocity gives displacement. The integral of speed gives distance.
• Some integrals can be found from simple shapes: triangles, rectangles, circles.

Steps

1. Going backwards
2. Signed area
3. Triangles
4. Half a circle
5. Area that cancels
6. Distance vs. displacement