The Definite Integral as Area

Guided Notes for this lecture

When we talk about area in the context of calculus, we need to expand our thinking about what area means in mathematics and what it represents in this context..

Next we will think about how to determine if area is positive or negative within the context of integrals and area under the curve.

Let's try a few more examples.

Now we need to consider the case of area between curves instead of area bounded by the x-axis.

At the end of this section you should be able to answer the following questions:

1. What does negative area mean in the context of a definite integral?
2. How can we determine net change based on positive and negative areas under the curve?
3. Why is the order in which we write the functions within our integral important when considering area under the curve?

Check Your Understanding
You should try these problems before reviewing the solutions to to these non-graded practice problems.