Cartoon Calculus: Ch 13 (The first fundamental theorem, revisited)

Quick links to Front matter, Back matter, and:
Part One: Ch 1: Introduction, Ch 2: Speed, Ch 3: Area, Ch 4: Fundamental theorem, Ch 5: Limits
Part Two: Ch 6: Derivatives, Ch 7: Toolkit, Ch 8: Extreme, Ch 9: Optimization, Ch 10: Economics
Part Three: Ch 11: Hard way, Ch 12: Easy way, Ch 13: Revisited, Ch 14: Physics, Ch 15: Conclusion

Page 159: Introductory page

Pages 160-161: It would be a bit too intense… // Story #1 is about a galloping horse.

Pages 162-163: One way to calculate average velocity… // Fortunately, we can find this limit…

Pages 164-165: But in addition to calculating average velocity… // We just covered two different ways…

Pages 166-167: Story #2 starts when we take two basic facts about circles… // We can use the tools from Chapter 7…

MB: p. 166 Draw a circle and a tiny ring around it of width dr. Area of ring is 2 pi r dr.

Pages 168-169: The next part of story #2 is about rings. // But another way to calculate the area of a ring…

MB: p. 169 The area of the ring is not the sum of the circumferences!!

Pages 170-171: Of course, these two ways to calculate area… // This story about area isn’t a proof…

MB: p. 171 Your analogy isn’t quite right: area= integral of circumference times thickness. Distance = integral of velocity times time.

Page 172: And there’s a bonus…

Quick links to Front matter, Back matter, and:
Part One: Ch 1: Introduction, Ch 2: Speed, Ch 3: Area, Ch 4: Fundamental theorem, Ch 5: Limits
Part Two: Ch 6: Derivatives, Ch 7: Toolkit, Ch 8: Extreme, Ch 9: Optimization, Ch 10: Economics
Part Three: Ch 11: Hard way, Ch 12: Easy way, Ch 13: Revisited, Ch 14: Physics, Ch 15: Conclusion

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