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Key Ideas:
Key Ideas:
Understand that an Integral finds the the area under a curve
Explain why the "area" may come up as negative and may not reflect the true area between two curves.
Understand how we can use infinite summation with discs to find the volume of a shape
The area under a curve
The area under a curve
The area under a curve can be determined by constructing a number of rectangles. We can then add the area's of these rectangles to estimate the are under the curve. In this way we can get an overestimate and an underestimate. Sometimes the average of the two is quite a good estimation for the exact area. If we want to obtain an even better estimate we can use a greater number of rectangles. Each rectangle will be narrower and hence the estimation improves.
What happens when the number of rectangles approaches infinity?
Important: This does NOT always find the area under a curve!!!! Do you know why not?
The fundamental theorem of calculus (FTC)
The fundamental theorem of calculus (FTC)
The fundamental theorem of calculus is also know as the F.T.C. And this is it:
Fundamental Theorem of Calculus
Fundamental Theorem of Calculus
Areas between curves
Areas between curves
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