Suppose that the rate of change of the reaction’s temperature at t seconds is given by C'(t) = 2e^(t/3) −3t. What is the change in temperature (in degree Celsius) over the first 6 seconds?

Question

Let C(t) denote the temperature of a chemical reaction at t seconds.

Answer 1

The accumulated change is the definite integral from 0 to 6

∫(2e^t/3 - 3t)dt =

2∫e^t/3dt - 3∫tdt =

6e^t/3 - 3t²/2 evaluated between 0 and 6 =

(6e^6/3 - 6e^0/3) - (3×6²/2- 3×0²/2) =

6e² - 60