A moment of silence for our great calculus - PowerPoint PPT Presentation

1 / 54
About This Presentation
Title:

A moment of silence for our great calculus

Description:

A moment of silence for our great calculus father please. OK here we go! First let s talk about what the integral means! Can you list some interpretations ... – PowerPoint PPT presentation

Number of Views:213
Avg rating:3.0/5.0
Slides: 55
Provided by: user265992
Category:

less

Transcript and Presenter's Notes

Title: A moment of silence for our great calculus


1
A moment of silence for our great calculus
father please.
2
OKhere we go!
3
Integrals Drill Practice
  • Im going to ask you about integrals.
  • Its important to be as fast as possible because
    time is your enemy .
  • When you think you know the answer,
  • (or if you give up ) click to get to
    the next slide to see if you were correct.

4
First lets talk about what the integral means!
  • Can you list some interpretations of the definite
    integral?

5
Heres a few facts
  • 1. If f(x) gt 0, then returns the
  • numerical value of the area between
  • f(x) and the x-axis (area under the curve)
  • F(b) F(a) where F(x) is
  • any anti-derivative of f(x).
  • (Fundamental Theorem of Calculus)
  • 3. Basically gives the total
    cumulative
  • change in f(x) over the interval a,b

6
What is a Riemann Sum?
  • Hint Heres a picture!

7
A Riemann sum is the area of n rectangles used to
approximate the definite integral.
  • area of n rectangles
  • As n approaches infinity
  • and
  • So the definite integral sums infinitely many
    infinitely thin rectangles!

8
The indefinite integral
  • ?

9
Wellhard to write easy to say
  • The indefinite integral equals the general
    antiderivative
  • F(x) C
  • Where F(x) f(x)

10
Now lets see if youve memorized specific
anti-derivatives that you will need to know
quickly during the AP exam.
11
sike!
  • I just made that one up to scare younow the rest
    will seem easy!

12
  • ?

13
ax C
  • I hope you got that one!

14
  • ?

15
C
  • Ready?

16
  • ??

17
- cos x C
  • Dont forget we are going backwards!
  • So if the derivative was positive, the
  • anti-derivative is negative.

18
  • ?

19
sin x C
  • Got the negative/positive situation straight??
  • Good!

20
  • ???

21
OK thats a hard one!
  • lntanxsec xC
  • If you got it right, you deserve a little treat!

22
  • ?

23
tan x C
  • That should have been easy!
  • Piece of cake! Upside down!!

24
  • ??

25
If you forget this onethink tan x sin x /
cos x
  • (then let u cos x, du - sin x dx, etc.)
  • ln(cos x) C
  • or
  • ln(sec x) C

26
  • ??

27
ln x C
  • You need the absolute value in case xlt0
  • Rise to the highest! Sursum ad Summum
  • yada yada

28
  • where n gt 1
  • Hint

29
1/xn x-n
  • sooooooo.
  • the answer is
  • C
  • You didnt say ln(xn) did ya??

30
  • ?

31
ex c
  • Easiest anti-derivative in the universe, eh?

32
  • ?

33
sec x C
  • Another easy peasy as a daisy anti-derivative!

34
  • ?

35
Not toooo difficult?
  • -cot x C
  • Safe landing?

36
  • ??

37
-csc x C
  • How are you holding up?
  • Bored out of your gourd?
  • Suck it up! Youll thank me when you test out of
    college calculus!

38
  • ???

39
  • C
  • Grin and bear it!! Ha Ha

40
  • OK! Take a deep breath! 5 more questions!

41
  • ?

42
tan-1x C
Keep it going!!
43
  • ?

44
sin-1x C
  • Oh yeah! Only 3 more to go.

45
  • ?

46
sec-1x C
Its all down hill now!!!!
47
(No Transcript)
48
  • (Did you get the significance of the picture?)

49
  • R U ready
  • 4 the last ?
  • ?

50
  • ???

51
  • A ln(x-a) B ln(x-b) C
  • (Im assuming you know how to find A B)

52
Youre done!
  • Ta Ta for now.

53
Be sure to check out these other power point
slide shows Derivatives Pre-Calculus Topics (on
a separate page) Sequences and Series Miscellaneou
s Topics and Additional BC Topics
54
  • I said you are done!
  • Stop clicking.
Write a Comment
User Comments (0)
About PowerShow.com