Remember that $\lim\limits_ { n \rightarrow \infty }\displaystyle \sum _ { i = 0 } ^ { n - 1 } f ( a + ( \Delta x ) i ) \Delta x = \int _ { a } ^ { b } f ( x ) d x$.

1. What does "$dx$" by itself represent?

   Hint (a):

   What is the connection between $dx$ and $Δx$?

2. What does the product $f(x)dx$ represent?

   Hint (b):

   What is the connection between $f(x)dx$ and $f(a + Δxi)Δx$?