Brainlag Plus
Brainlag PlusArea under a curve
Estimate the area under a curve by splitting it into trapezia, say whether the estimate is too big or too small, and interpret the area as a distance or a total amount.
Strips and trapezia
Split the area into strips of equal width h. Join the tops of each strip with a straight line, so each strip is a trapezium with area ½ × h × (a + b), where a and b are the heights at its two edges. Add the trapezia.
A car's speed is read every 2 seconds:
- speeds at t = 0, 2, 4, 6, 8: 0, 6, 10, 12, 12
- ½ × 2 × (0 + 6) = 6
- ½ × 2 × (6 + 10) = 16
- ½ × 2 × (10 + 12) = 22
- ½ × 2 × (12 + 12) = 24
- distance ≈ 6 + 16 + 22 + 24 = 68 m
The quick form: ½ × h × (first + last + 2 × the middle heights) = ½ × 2 × (0 + 12 + 2 × 28) = 68.
The rest of this lesson and its 8 practice questions are in Plus.
Screen 1 of 5, free to read.
- 8 exam-style questions, marked as you go, each with a worked solution
- Anything you get wrong is saved to your flashcards