Average concentration
A concentration is C(t)=10e^(-0.2t) mg/L for 0<=t<=5. Average value is (1/5) integral_0^5 C(t)dt.
- An antiderivative is -50e^(-0.2t).
- Evaluate endpoints.
- Divide by interval length.
area, volume, average value, and net change
A concentration is C(t)=10e^(-0.2t) mg/L for 0<=t<=5. Average value is (1/5) integral_0^5 C(t)dt.
Pause. Find what matters. Then make your move.