Area between curves
On 0<=x<=2, y=2x lies above y=x^2. Area = integral_0^2(2x-x^2)dx.
- Top minus bottom.
- Find intersections at 0 and 2.
- Evaluate x^2-x^3/3.
area, volume, average value, and net change
On 0<=x<=2, y=2x lies above y=x^2. Area = integral_0^2(2x-x^2)dx.
Pause. Find what matters. Then make your move.