What you need to do: There are standard integrals for certain functions specified by the course that you need to learn.
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See below for a list of some not in the formula book (written in computerised maths).
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Syllabus requires you: To be able to apply these standard integrals for definite and indefinite integrals.
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Don't forget the +C for indefinite integrals (ones without limits), it's worth one mark in a WJEC exam if you forget that small bit! But generally, it's good maths not to forget.
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Please note: All of the following integrals are indefinite, and so should have an unknown +c on the end.
Function
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Integral
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x^n
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(x^n+1) / (n+1)
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(ax+b)^n (n is not -1)
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(ax+b)^n+1 / a(n+1)
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sin (x)
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-cos (x)
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sin (ax+b)
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-(1/a)*cos(ax+b)
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cos (x)
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sin (x)
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cos (ax+b)
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(1/a)*sin(ax+b)
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Sec^2 (x)
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tan (x)
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Sec^2 (ax+b)
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(1/a)*tan(ax+b)
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e^x
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e^x
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e^(ax+b)
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(1/a)*e^(ax+b)
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1/x
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ln|x|
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1/(ax+b)
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(1/a)*ln|ax+b|
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1/((x^2)+1)
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tan^-1 (x)
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1/([the square root of] [1- X^2])
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sin^-1 (x)
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-1/([the square root of] [1-X^2]) |
cos^-1 (x) |
Note that all of these ( in particular the bottom 3 ) are a reverse of the differential standards you are also required to learn ( the bottom 3 you are required to be able to prove).
The key for the table is standard keyboard maths, where:
"/" means divided.
"*" means multiply.
"(...)" indicate a particular part that is kept together i.e. (...)/(...) means everything in the top brackets is divided by everything in the bottom brackets.
"^" means raise to the power of (or in the case of sin^-1, for example, the inverse sine function).
"[the square root of] [...]" Implies the following square bracket is all within the square root sign.
And space helps to seperate parts of the functions and their standard integrals.
For a less complex looking/easier to understand version of these I suggest looking at a hand-written copy of the standard integrals.
[Link to C3 past papers]
Comments (2)
Luke said
at 7:41 pm on Sep 25, 2012
Hope this helps you out Mrs Richards, considering this page was blank before.
Luke said
at 7:49 pm on Sep 25, 2012
Well, helps you out in terms of saving you time rather than teaching you this, after all, YOU taught ME this haha XD
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