A moment of silence for our great calculus

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A moment of silence for our great calculus
father please.
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OKhere we go!
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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.

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First lets talk about what the integral means!

• Can you list some interpretations of the definite
  integral?

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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

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What is a Riemann Sum?

• Hint Heres a picture!

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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!

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The indefinite integral

• ?

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Wellhard to write easy to say

• The indefinite integral equals the general
  antiderivative
• F(x) C
• Where F(x) f(x)

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Now lets see if youve memorized specific
anti-derivatives that you will need to know
quickly during the AP exam.
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sike!

• I just made that one up to scare younow the rest
  will seem easy!

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• ?

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ax C

• I hope you got that one!

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• ?

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C

• Ready?

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• ??

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- cos x C

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

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• ?

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sin x C

• Got the negative/positive situation straight??
• Good!

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• ???

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OK thats a hard one!

• lntanxsec xC
• If you got it right, you deserve a little treat!

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• ?

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tan x C

• That should have been easy!
• Piece of cake! Upside down!!

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• ??

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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

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• ??

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ln x C

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

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• where n gt 1
• Hint

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1/xn x-n

• sooooooo.
• the answer is
• C
• You didnt say ln(xn) did ya??

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• ?

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ex c

• Easiest anti-derivative in the universe, eh?

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• ?

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sec x C

• Another easy peasy as a daisy anti-derivative!

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• ?

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Not toooo difficult?

• -cot x C
• Safe landing?

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• ??

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-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!

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• ???

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• C
• Grin and bear it!! Ha Ha

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

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• ?

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tan-1x C
Keep it going!!
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• ?

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sin-1x C

• Oh yeah! Only 3 more to go.

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• ?

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

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• R U ready
• 4 the last ?
• ?

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• ???

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

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Youre done!

• Ta Ta for now.

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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
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• I said you are done!
• Stop clicking.