1. 請列舉三種質化研究方法，說明並舉例：(a) 其如何被操作；(b) 其主要可以協助研究者發掘那些人、事、物的特殊性？(60 分)

1. (10%) Let f(x) be a differentiable function as shown in Figure 1. It needs to compute the integral $\int_{a}^{b} f(x)dx$. For some reason, the integration is not possible. We decide to linearize f(x) at x = a$ and use the trapezoidal area $A$ to approximate the integral, i.e. $ \int_{a}^{b} f(x) dx \approx A $. Please find the area A.