Integration Yr2 Flashcards
Reverse chain rule
When is reverse chain rule applicable?
If some form of derivative is hanging outside
How do you integrate using reverse chain rule on trig?
Look at the question and what has been raised to a power
Make y this only (+1 to power)
Then differentiate, remember because it is trig it is an enclosed function
See what need altering and include this in final answer (y)
How do you integrate using reverse chain rule on Exponentials?
Make y the e ^ power bit
Differentiate this and see if the outside bit is a multiple of whatever is in the question
If so, add altriification to your y
Remember + c
How do you integrate reciprocals using reverse chain rule?
Look at denominator
Differentiate this, if some multiple of this is in the denominator then put the denominator in a ln ||
How do you integrate with respect to y?
Rearrange the equation from y= to x=
Then change limits to y axis ones
Integrate normally
Memorise the table
What is one rule when dealing with reverse chain rule?
You cannot divide by a variable. In other words only works when some multiple of inner derivative is sticking out front
What is the trig identity relating sec ^2 (x) and tan ^2 (x)?
Sec^2 = 1 + tan^2
(Tripple line equals sign)
What is the trig identity relating cosec ^2 and cot^2?
Cosec^2(x) = 1 + cot^2(x)
(Tripple line equals sign)
What is the strategy for whenever you see integral of tan^2 (x)?
What is strategy for whenever you see integral of cos^(x) or sin^2(x)?
What happens to sec^2 when differentiated?
The power does not go down
What are the steps to doing integration by substitution?
- Make substitution of u
- Find du/dx
- Rearrange for dx
- Put this into the integral equation
5.integrate normally - Put the u back in
Using substitution do
Using integration by substitution do these
What do you have to remember when using substitution with definite integrals?
Change the limits in terms of u aswel
What is the integration by parts formula?
What is the rule for determining the u (integration by parts)?
LATE
Solve using integration by parts
In this case which one do we choose as u?
Th more simpler expression
Importance of notation
Why can you not integrate these trig functions directly and what instead must you use for them?
Reverse chain rule is not applicable?
