### Home > CALC > Chapter 1 > Lesson 1.3.1 > Problem 1-109

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. Homework Help ✎Explain why your choice will determine the best approximation for the area.

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

**Left Endpoint Rectangles****Midpoint Rectangles****Right Endpoint Rectangles**

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

Midpoint Rectangles

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?