Integration Flashcards
what does this standard integration formula =
what does this integration forumla =
What does this integration formula =
What is integration by inspection (GDA)
Guess > guess what the integration would be
Differentiate > differentiate your guess
Adjust > if you differentiation doesn’t look like the thing you were told to differentiate, adjust it so it does
How do you do integration by partial fractions
> complete partial fractions
then GDA to integrate
Will most likely be a ln
What acronym should you always use when integrating
L - Logs
A - Algebra
T - Trig
E - Exponentials
How to do integration by substitution without limits
Steps:
1) differentiate u, then adjust to make dx the subject
2) substitute dx into the integration
3) simplify the expression
4) then integrate
5) then replace u to form the whole expression
If it doesnt have any limits the answer should have + C
How to do integration by substitution with limits
Steps:
1)differentiate u by du/dx then make dx the subject, also then use the lmits given as x values to sub into the u = equation to get the new limits
2) substitute dx into the integration
3) simplify the expression
4) integrate
5) use the limits and find a full answer
If the question has = a number like this example that is what you should end up with
What do you need to do when you are not given a substitution
how to do integration by substitution without a substitution
Steps;
1) Pick your u, using LATE and from experience with questions
2) same as the other integrations differentiate u and make dx the subject, if you are given limits substitute them into u = to get the new limits
3) substitute dx into the integration
4) simplify the expression
5) after simplifying something left that isn’t u is part of the u equation
6) adjust the u equation to solve for this number and then substitute that answer back into the integration (this is the second substitution)
7) simplify then integrate
If it has limits find C if not leave it with + C
What is a general trick for these integration questions only trig
Steps:
1) factor out the derivative of the trig function with the highest power
2) integrate the remaining function as if it was a polynomial
remember you can always substitute like in the answer in the photo
How do you integrate these questions
Must use the cos double angle formula!
> then make cos or sin the subject and substitute it back in,now you can integrate
what is the cos double angle formula ( 3 variations)
What does the L stand for in the acronym Late and what should you do when using L
What does the A stand for in the acronym Late and what should you do when using A
(3 things)
stand for algebra
3 things to do:
1) standard results (GDA)
2) Small manipulation
> something/ 1 and then split it = something/1 + something/1 (in the photo)
3) partial fractions
What does the T stand for in the acronym Late and what should you do when using T
Trig, and that is using the 6 derivatives
What does E stand for in the acronym LATE and what should you do when using E (3 things)
Stands for exponetials
1) integration using substitution
2) integration by parts
3) trapezium rule
What is the integration by parts formula
How to solve an integration by parts question
Steps:
1) choose u and dv/dx, by using LATE
2) differentiate u and integrate dv/dx
3) put them into the formula for integration by parts
4) integrate the second part of the equation( this may make you have to do the technique twice - just set it out clearly and you won’t get confused
5) simplify and put + c, unless there are limits
Area of a trapezium formula
you will be directly asked for the trapezium rule to be used
What is h in the trapezium rule
h is the equally spaced gap between each line
to find h:
find the difference between 2 x values and h should be the same for every gap
What is y in the trapezium rule
y is each line of a trapezium
How to solve a trapezium rule question
steps:
1) Make a table if one is not given (you should have 5 values if it asks for 4 segments, that how to know if your table is right)
2) find the y values in your table by substituting each X value in
3) find h by finding the difference between 2 X values
4) then put it in the equation
