Area Between Curves. Area Between Curves With a few modifications, we can extend the application of definite integrals from the area under a curve to.

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Presentation transcript:

Area Between Curves

Area Between Curves With a few modifications, we can extend the application of definite integrals from the area under a curve to the area of a region between two curves. Take a look at the diagram below …

Stated formally, Let’s look at an example … Take a moment to graph on your calculator. Keep boundaries in mind.

Your graph should look something like this: Write the integral and evaluate it.

In the previous example, the curves never intersected. The next example considers this new scenario. Example 2: Take a look at the graph: Q: What information is still needed? A: the boundaries between which to integrate. Using TI-83’s & TI-84’s you might see these visually or using TABLE function.

The best way to discern boundaries is algebraically. Set the two function equal to each other and solve for x. Now that boundaries are ascertained, integrate! The End