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C3 INTEGRATION (2)

Page history last edited by Luke 11 years, 6 months ago Saved with comment
What you need to do: There are standard integrals for certain functions specified by the course that you need to learn.
  See below for a list of some not in the formula book (written in computerised maths).
Syllabus requires you: To be able to apply these standard integrals for definite and indefinite integrals.
 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.

 

Please note: All of the following integrals are indefinite, and so should have an unknown +c on the end.

 

Function
Integral
x^n
(x^n+1) / (n+1)
(ax+b)^n (n is not -1)
(ax+b)^n+1 / a(n+1)
sin (x)
-cos (x)
sin (ax+b)
-(1/a)*cos(ax+b)
cos (x)
sin (x)
cos (ax+b)
(1/a)*sin(ax+b)
Sec^2 (x)
tan (x)
Sec^2 (ax+b)
(1/a)*tan(ax+b)
e^x
e^x
e^(ax+b)
(1/a)*e^(ax+b)
1/x
ln|x|
1/(ax+b)
(1/a)*ln|ax+b|
1/((x^2)+1)
tan^-1 (x)
1/([the square root of] [1- X^2])
 sin^-1 (x)
-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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