What lessons should you know before studying integrals?

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Discussion Overview

The discussion revolves around the preparatory knowledge and concepts that participants believe are important before studying integrals, particularly in the context of calculus. It includes considerations of logarithms, derivatives, and the relationship between these topics.

Discussion Character

  • Exploratory, Homework-related, Conceptual clarification

Main Points Raised

  • One participant expresses a desire to study integrals after completing limits and derivatives but is unsure about the necessity of logarithms.
  • Several participants suggest that studying logarithms is essential before tackling integrals, with one noting that logarithms are typically taught just before integrals in their educational system.
  • Another participant mentions the importance of understanding the relationship between integrals and derivatives, suggesting they are fundamentally connected.
  • There is a mention of the need to revisit the exponential function after learning about logarithms, particularly in the context of solving ordinary differential equations (ODEs).
  • One participant humorously suggests learning to use Mathematica or consulting a comprehensive integral table as alternative resources.
  • Another emphasizes the importance of mastering trigonometric and hyperbolic functions, along with the properties of logarithms and exponents.

Areas of Agreement / Disagreement

Participants generally agree on the importance of understanding logarithms before studying integrals, but there is no consensus on the exact prerequisites or the depth of knowledge required in derivatives and other topics.

Contextual Notes

Some participants reference specific educational practices in their countries, which may influence their perspectives on the order of learning these mathematical concepts. There is also a variation in the perceived difficulty of integrals compared to derivatives.

Who May Find This Useful

Students preparing to study integrals, educators looking for insights on prerequisite knowledge, and individuals interested in the connections between different calculus concepts.

Andrax
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so this year I've finshed limits , derivatives (that's it in cacylus)and i'd like to study integrals , ididn't study logarithms yet so idk if that's necessary, thanks
 
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Go ahead and take a couple of days to study logs. The integrals will still be there when you get finished.
How thoroughly did you study derivatives without knowing logs or what logarithmic differentiation was?
 
SteamKing said:
Go ahead and take a couple of days to study logs. The integrals will still be there when you get finished.
How thoroughly did you study derivatives without knowing logs or what logarithmic differentiation was?
in my country (france), logarithms are @ last year of high school just before integrals , that's why, i didn't learn logarithmic differentiation but I've learned most important deriv laws (l'hospital etc..), i like english books better than france ones , better exaplanation , simpler notations etc..
i'll focus on logarithms
 
You may want to go over the e^x stuff again after learning about logs. Logs are also used when you separate variables to solve ODE's, so you really need to know them well.
 
I'm no expert, but don't basic integrals integrals and derivatives go together? Sure integrals are harder in general (hence the need for humongous tables), but at the basic level they are two sides of the same coin. Heck, Apostol talks about integrals for 300 pages before introducing derivatives.
 
lots of trig
 
You should learn how to install and operate Mathematica on your computer.

An alternate option is going online and learning to purchase Gradshteyn and Ryzhik and open it to its table of contents.

:-p

But if you really want to do them yourself, be a master of manipulating trigonometric and hyperbolic functions. Know and understand the properties of logarithms and exponents.
 

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