-Antidifferentiation- Chapter 6

1
-Antidifferentiation-Chapter 6
?????? ????? ??? ??
2
Introduction to Antidifferentiation (1)

• ??(????)????????
• ????????,?????,??????????

??
???
????
??
??
???
EX ???
3
Introduction to Antidifferentiation (2)

• ??????????,???????
• ??????, ??????????x, ??????????
• ?????????(?????)

???x, ??1
?????, ???(antidifferentiation)??????????
4
Introduction to Antidifferentiation (3)

• Leibniz(????)???????????????
• ,? ????????????,? ???
• ? x ?????(indefinite
  integral),???(power
• rule)??

EX
5
Introduction to Antidifferentiation (4)

• ???????(???)????(k, c??constant)

k???
1
EX
2
EX
3
EX
6
Introduction to Antidifferentiation (5)
4
EX
5
k constant
6
7
EX
7
Introduction to Antidifferentiation (6)
8
EX
9
EX
EX
EX
8
????
1
2
3
4
9
6-2 Some Application of Antidifferentiation (1)

• ???????,???? ?????
• ?????????? ???????

?
EX
? , ?
sol
?? , ??c
???
10
6-2 Some Application of Antidifferentiation (2)
EX
???????2x??(3,11)???, ????
sol
???????????
??
11
6-2 Some Application of Antidifferentiation (3)
EX Obtaining cost from marginal cost???????x
units???marginal cost?
. ?????(?????????????)?700?, ???
??x units??????
1
??10?units??????
2
sol
??marginal cost??cost?????
1
????????????700????
2
12
6-2 Some Application of Antidifferentiation (4)
EXRocket Flight???????????????300feet/sec,
????? ????????-32feet/sec2
????????(????)
1
????????(???)
2
sol
????(v)? feet/sec, ???(a)?
feet/sec2
1
??????????
or
, ??c
???
? ?
???????
13
6-2 Some Application of Antidifferentiation (5)
sol ??3????????(??????????????)??
????, ?????????, ??????????.
2
or
?c