2.6 Approximating areas

Applet explorations

1) The goal of this activity is to consider alternative methods of approximating areas under curves. 2) Use the dropdown menu to change the shapes for your approximation and use the slider to change the number of shapes used in this approximation. 3) Can you work out how each of the methods are approximating the area under the function? Which method best approximates the area for this function? Are they overestimates or underestimates of the actual area for each one? 4) Change the function. Is the same method always the best for every function? Consider carefully the advantages and disadvantages for each method. Summarise any key points at the bottom of the page.

Applet conclusions

Note any key points from this activity. How can this applet be used to develop our understanding of calculus?