Cartoon Calculus: Ch 11 (Integration the hard way)

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 131: Part Three (introductory page)

Page 133: A journey of a thousand miles…

Pages 134-135: In Part One, we learned… // The hard way is to directly climb Mt. Integral.

Pages 136-137: The way to directly climb Mt. Integral… // The trick is to add more and more rectangles…

Pages 138-139: Of course, there are many different paths up a mountain… // In the same way, there are…

Pages 140-141: As an example, let’s return… // This example turns out to be lucky…

Pages 142-143: That example may not have seemed too hard… // That may seem impossible…

Pages 144-145: So let’s return to the same mountain… // Once again we’re lucky…

Page 146: That’s it!

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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