April 2023
Beginner to intermediate
656 pages
17h 28m
English
Content preview from Calculus All-in-One For Dummies (+ Chapter Quizzes Online)
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Chapter 18
Taming the Infinite with Improper Integrals
IN THIS CHAPTER
The hospital rule — in case studying calculus makes you ill
Meeting integrals without manners
The paradox of Gabriel’s horn
The main topic of this chapter is really amazing when you stop and think about it: calculating the area (or volume) of shapes that are infinitely long. The word infinity comes up in mathematics so often that perhaps we become jaded about the concept and forget how truly incredible it is. It’s about 93 million miles from the Earth to the Sun. That distance is so great that it’s nearly impossible to wrap our minds around it, but it’s nothing compared to the distance to Alpha Centauri A (the nearest star), which is 4.24 light-years away — about 268,000 times as far as the distance to the Sun. Our Milky Way Galaxy is about 100,000 light-years across, and it’s about 4.5 million light-years to our nearest spiral galaxy neighbor, the Andromeda Galaxy. Go out about 10,000 times that far and you reach the “edge” of the observable universe at about 46 or 47 billion light-years away. That’s definitely quite a ways out there, but it’s nothing compared to infinity.
The shapes you deal with in this chapter ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.