But just as much as it is easy to find the differential…
![“But just as much as it is easy to find the differential [derivative] of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not.” quote by Johann Bernoulli](https://sms4smile.com/q/img-quotes/324/johann-bernoulli-74276_calculus_but-just-as-much-as-it-is-easy-to-find-t_3054028.png)
“But just as much as it is easy to find the differential [derivative] of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not.”
About This Quote
This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation.
Differentiation is straightforward, but integration can be uncertain or impossible.
In simple terms: Finding derivatives is easy; finding antiderivatives can be hard.
Key Takeaway
Recognize limits of solvability.
Themes
mathematics
calculus
uncertainty
Mood
analytical
reflective
Type
educational
philosophical
When to use this quote
- solving physics problems
- engineering design
- economic modeling
- educational instruction
Key Concepts
analysis
integration
existence
Questions to Reflect On
- When is approximation acceptable?
- How to decide if a problem is solvable?
A Different Perspective
Not all functions have elementary antiderivatives, requiring approximation.