Integration Yr2

Question 1

Reverse chain rule

Answer 1

Question 2

When is reverse chain rule applicable?

Answer 2

If some form of derivative is hanging outside

Question 3

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Question 4

How do you integrate using reverse chain rule on trig?

Answer 4

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)

Question 5

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Question 6

How do you integrate using reverse chain rule on Exponentials?

Answer 6

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

Question 7

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Question 8

How do you integrate reciprocals using reverse chain rule?

Answer 8

Look at denominator
Differentiate this, if some multiple of this is in the denominator then put the denominator in a ln ||

Question 9

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Question 10

How do you integrate with respect to y?

Answer 10

Rearrange the equation from y= to x=
Then change limits to y axis ones
Integrate normally

Question 11

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Question 12

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Question 13

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Question 14

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Question 15

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Question 16

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Question 17

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Question 18

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Question 19

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Question 20

Memorise the table

Question 21

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Question 22

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Question 23

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Question 24

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Question 25

What is one rule when dealing with reverse chain rule?

Answer 25

You cannot divide by a variable. In other words only works when some multiple of inner derivative is sticking out front

Question 26

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Question 27

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Question 28

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Question 29

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Question 30

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Question 31

What is the trig identity relating sec ^2 (x) and tan ^2 (x)?

Answer 31

Sec^2 = 1 + tan^2
(Tripple line equals sign)

Question 32

What is the trig identity relating cosec ^2 and cot^2?

Answer 32

Cosec^2(x) = 1 + cot^2(x)
(Tripple line equals sign)

Question 33

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Question 34

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Question 35

What is the strategy for whenever you see integral of tan^2 (x)?

Answer 35

Question 36

What is strategy for whenever you see integral of cos^(x) or sin^2(x)?

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Question 37

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Question 38

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Question 39

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Question 40

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Question 42

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Question 43

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Question 45

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Question 47

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Question 48

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Question 49

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Question 50

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Question 51

What happens to sec^2 when differentiated?

Answer 51

The power does not go down

Question 52

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Question 53

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Question 54

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Question 55

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Question 56

What are the steps to doing integration by substitution?

Answer 56

1. Make substitution of u
2. Find du/dx
3. Rearrange for dx
4. Put this into the integral equation
   5.integrate normally
5. Put the u back in

Question 57

Using substitution do

Answer 57

Question 58

Using integration by substitution do these

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Question 59

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Question 60

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Question 61

What do you have to remember when using substitution with definite integrals?

Answer 61

Change the limits in terms of u aswel