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In this lesson, we explore the integral as a method to accumulate a set of changes over an interval. We define the integral as the anti-derivative, where F’(x) = f(x). By applying a sequence of changes from point a to point b, we derive a function F(x) that represents the accumulated area or change. We also calculate the area and perimeter of figures, using examples like squares to illustrate these concepts. This lesson aims to reinforce our understanding of how areas are calculated and how integrals help in understanding functions and their changes.
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BEX Calculus Course Lesson 4
1 x dx
1 dx r r p dp dx x
1 3 5 7
= 1 + 3 + 5 + 7 + 9 5x5
= 5 + 7 + 9 5x5 - 2x2 The integral (accumulating a set of changes) Can be found with the anti-derivative[a function where F’(x) = f(x)]
Applying a sequence of changes (f(x))from a to b Getting a function that changes the same way (F(x))and taking the difference Is the same as
x 20 Area = 20x x Area = ½ * 40 * x = 20x 40
1d Perimeter Change 2d Area Change 1 x x
