integration

Question 1

• Definite integrals

 Areas under the x axis

Answer 1

Integrate separately + take positive value

Question 1

Standard functions

Answer 1

Question 2

definite integrals

Areas between line + curve

Answer 2

Figure out which is on top

Find points of intersections

Question 3

Integration as the limit of a sum

Answer 3

Question 4

Reverse chain rule

Answer 4

Question 5

when does reverse chain rule work

Answer 5

normal function

some multiple of the derivative of the inside function on the outside of the bracket

numerator is derivative of the denomiator

Question 6

reverse chain rule examples

Answer 6

Question 7

Why does 1/x integrate to ln MODULUS x?

Answer 7

Because when you differentiate it there is this extra condition we don’t right. Mod X just maintain the domain of the function

Question 8

Integration by substitution

Answer 8

Question 9

Integration by parts

Answer 9

Question 10

NOTATION FOR DEFINATE

Answer 10

Question 11

by parts remember

Answer 11

you want du/dx to be simple to integrate so make U the simple one in the initial equation

Question 12

Integrate log x

Answer 12

Question 13

Integrating tan + cot

Answer 13

Question 14

Integration by parts twice

Answer 14

could bring integral brackets together

Question 15

differential equations

Answer 15

split up variables

REMEMBER PLUS C

Question 16

integrate log x when there is a power of something

Answer 16

Question 17

PLUS C