The Height With the Same Area

You'll learnto read an average value as the height of the rectangle that encloses the same area, to divide by the length of the interval rather than by anything else, and to check your answer against the values the function actually takes.

An integral is an area. An average value is a height. One division separates them, and it is the step that goes missing most often in this unit. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · DIVIDE BY THE LENGTH, THEN CHECK IT IS A VALUE OF f · v2

The average value is the height of the rectangle that fences off the same area

Before you start

What you're looking at

A curve, the region under it, and a violet rectangle standing on the same base. The rectangle grows until the two shapes enclose the same area.

The question

What flat height would fence off that same area, and could the function itself ever equal it?

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