Accumulation from a rate
Water enters a tank at r(t)=3t^2+2 liters/minute for 0<=t<=2. Total added water is integral_0^2 r(t)dt = [t^3+2t]_0^2.
- Integrate the rate over time.
- Evaluate upper minus lower.
- Units become liters.
definite integrals and the Fundamental Theorem
Water enters a tank at r(t)=3t^2+2 liters/minute for 0<=t<=2. Total added water is integral_0^2 r(t)dt = [t^3+2t]_0^2.
Pause. Find what matters. Then make your move.