CPM Homework Help : CALC3RD Problem 8-4

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

What does " $dx$ " by itself represent?
Hint (a):
What is the connection between $dx$ and $Δx$ ?
What does the product $f(x)dx$ represent?
Hint (b):
What is the connection between $f(x)dx$ and $f(a + Δxi)Δx$ ?

First quadrant graph, increasing curve opening up, starting about 1 fourth up on y axis, & 3 vertical shaded bars of equal width, bottom edges on x axis, left edge of first bar labeled, a, right edge of last bar labeled, b, top left vertex of each bar, on the curve.