WHICH IS BETTER? Part One
Below are different sets of rectangles to approximate the same area under a curve for $f(x)$. Look at the three different sets of rectangles and decide which will best approximate $A(f, a ≤ x ≤ b)$ for this function.

1. Explain why your choice will determine the best approximation for the area.

   Hint (a):

   Which graph is the closest to the exact area under the curve?

   Answer (a):

   Midpoint Rectangles

2. Will left endpoint rectangles always be an underestimate for any function? Explain.

   Left Endpoint Rectangles

   

   Midpoint Rectangles

   

   Right Midpoint Rectangles

   

   Hint (b):

   Notice that the graphs in the diagrams above show an increasing function. That is, as $x$ increases, the $y$-values increase. What if we graphed a decreasing function instead? Would left-endpoint rectangles be underestimates then?