Measuring Length Change: Definite Integrals in Continuous Growth Analysis
To find the total change in length over a time interval, we use definite integrals to capture continuous growth or contraction. Given a rate of change function \(\frac{dL}{dt}(t)\), the total change in length, \(\Delta L\), from time \(a\) to \(b\) is calculated by integrating this function over the interval: \([\Delta L = \int_{a}^{b} \frac{dL}{dt}(t) \, […]