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1 year ago

So year 2 integration is pretty tough because there are so many methods to doing a question and all of them give different answers so how do you know which method to do because I waste so much time doing different methods and getting different answers then it is just a mess

Any advice? Thankss

Any advice? Thankss

There are a few cheat sheets like

https://www.drfrostmaths.com/uploads/JFrost/files/C4CheatSheet.pdf

https://tutorial.math.lamar.edu/pdf/calculus_cheat_sheet_all.pdf

http://www.cheat-sheets.org/saved-copy/Calculus_Cheat_Sheet_Integrals_Reduced.pdf

And for many questions, the approach should be reasonably clear if you think a couple of steps ahead about whether its going to work (and clearly list potential approaches).

https://www.drfrostmaths.com/uploads/JFrost/files/C4CheatSheet.pdf

https://tutorial.math.lamar.edu/pdf/calculus_cheat_sheet_all.pdf

http://www.cheat-sheets.org/saved-copy/Calculus_Cheat_Sheet_Integrals_Reduced.pdf

And for many questions, the approach should be reasonably clear if you think a couple of steps ahead about whether its going to work (and clearly list potential approaches).

(edited 1 year ago)

Reply 2

1 year ago

Original post by Idk131

So year 2 integration is pretty tough because there are so many methods to doing a question and all of them give different answers so how do you know which method to do because I waste so much time doing different methods and getting different answers then it is just a mess

Any advice? Thankss

Any advice? Thankss

you could make a list of all the integration methods, I would make one for differentiation too but on a separate sheet so I dont get confused. write down all examples of integration like substitution, parts, trigonometric etc. then next to each type write a couple examples and the conditions that fulfill that method.

for example=

you see two functions multiplied together such as e^xsin2x , it’s by parts.

making a lietarlly list will help u in the exam as u can think back to it.

try to understand why each method is used, don’t just memorise the methods, you will get it in the end. )

Reply 3

1 year ago

Couple comments:

(i) The tricky thing about indefinite integrals is that you could end up with different answers with different methods, but all are correct since a hidden constant might prop up somewhere. As long as your method is good, you're good. In fact, if the solution to an indefinite integral is x^2+C, you could have very well written down x^2+10000000+C just to annoy your teacher - technically correct, but why though.

I think there is a classic example of integrating sin(2x) using very different methods, and it will yield different results, but in essence are the same, since they all differ by some constants.

Sidenote: Definite integrals do poses some problems, but at the end of the day it still doesn't matter which path you choose as long as your bounds of integration are adjusted appropriately.

(ii) Another thing with learning so many methods and techniques is not a problem about calculus itself. For all we know, we could only read off the standard result of integrals from a table (or commit to your memory). All these fancy techniques like IBP, u-sub, trig sub and partial fractions is to make something we can't read the result off of the integral table to something we can. As to how we get there, it doesn't matter. Though I should mention, as previous posters would agree, some "shapes" of the integrand do require some specific techniques, which is why practice is so important.

Many people would say, and I concur, "calculus is easy, the hard part is the algebra".

(i) The tricky thing about indefinite integrals is that you could end up with different answers with different methods, but all are correct since a hidden constant might prop up somewhere. As long as your method is good, you're good. In fact, if the solution to an indefinite integral is x^2+C, you could have very well written down x^2+10000000+C just to annoy your teacher - technically correct, but why though.

I think there is a classic example of integrating sin(2x) using very different methods, and it will yield different results, but in essence are the same, since they all differ by some constants.

Sidenote: Definite integrals do poses some problems, but at the end of the day it still doesn't matter which path you choose as long as your bounds of integration are adjusted appropriately.

(ii) Another thing with learning so many methods and techniques is not a problem about calculus itself. For all we know, we could only read off the standard result of integrals from a table (or commit to your memory). All these fancy techniques like IBP, u-sub, trig sub and partial fractions is to make something we can't read the result off of the integral table to something we can. As to how we get there, it doesn't matter. Though I should mention, as previous posters would agree, some "shapes" of the integrand do require some specific techniques, which is why practice is so important.

Many people would say, and I concur, "calculus is easy, the hard part is the algebra".

(edited 1 year ago)

Original post by tonyiptony

Couple comments:

Many people would say, and I concur, "calculus is easy, the hard part is the algebra".

Many people would say, and I concur, "calculus is easy, the hard part is the algebra".

I once read a quote that was something along the lines of "differentiation is a skill; integration is an art".

Give me any combination of A level functions added, multiplied, exponentiated etc and I can be confident of finding the derivative, even if it involves some horrible algebra. But integration is a different beast entirely - once you get past standard functions that can be integrated on sight like polynomials, sin and cos, plus e^x then you get into the realms of things that can't be integrated at all (e^(x^2), log(sin x) etc), or things that are not at all obvious at first sight. There is really no substitute for practice, practice, practice when it comes to integration

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