Title: Welcome to the Integral Drill and Practice Power Point Flash Drill!
1Welcome to the Integral Drill and Practice Power
Point Flash Drill!
- Developed by Susan Cantey
- at Walnut Hills H.S.
- 2006
2A moment of silence for our great calculus
father please.
3OKhere we go!
4Integrals 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.
5First lets talk about what the integral means!
- Can you list some interpretations of the definite
integral?
6Heres 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
7What is a Riemann Sum?
8A 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!
9The indefinite integral
10Wellhard to write easy to say
- The indefinite integral equals the general
antiderivative - F(x) C
- Where F(x) f(x)
11Now lets see if youve memorized specific
anti-derivatives that you will need to know
quickly during the AP exam.
12sike!
- I just made that one up to scare younow the rest
will seem easy!
13 14ax C
15 16 C
17 18- cos x C
- Dont forget we are going backwards!
- So if the derivative was positive, the
- anti-derivative is negative.
19 20sin x C
- Got the negative/positive situation straight??
- Good!
21 22OK thats a hard one!
- lntanxsec xC
- If you got it right, you deserve a little treat!
23 24tan x C
- That should have been easy!
- Piece of cake! Upside down!!
25 26If 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
27 28ln x C
- You need the absolute value in case xlt0
- Rise to the highest! Sursum ad Summum
- yada yada
29 301/xn x-n
- sooooooo.
- the answer is
- C
- You didnt say ln(xn) did ya??
-
31 32ex c
- Easiest anti-derivative in the universe, eh?
33 34sec x C
- Another easy peasy as a daisy anti-derivative!
35 36Not toooo difficult?
37 38-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!
39 40- C
- Grin and bear it!! Ha Ha
41- OK! Take a deep breath! 5 more questions!
42 43tan-1x C
Keep it going!!
44 45sin-1x C
- Oh yeah! Only 3 more to go.
46 47sec-1x C
Its all down hill now!!!!
48(No Transcript)
49- (Did you get the significance of the picture?)
50 51 52- A ln(x-a) B ln(x-b) C
- (Im assuming you know how to find A B)
53Youre done!
54Be 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
55- I said you are done!
- Stop clicking.