Clicker Question 1

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Clicker Question 1

• Are you here?
• A. Yes
• B. No
• C. Not sure

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Clicker Question 2

• What is the derivative function of f (t)
  sin(3t 2 5) ?
• A. cos(3t 2 5)
• B. -cos(3t 2 5)
• C. 6t cos(3t 2 5)
• D. -6t cos(3t 2 5)
• E. cos(6t)

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Clicker Question 3

• What is the most general antiderivative of f (x)
  x 5 4 x -2 ?
• A. 5x 4 2x -3 C
• B. 1/5 x 6 4x ½ x -1 C
• C. 1/6 x 6 4x x -1 C
• D. 1/6 x 6 4x - x -1 C
• E. Im clueless

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Clicker Question 4

• What is the most general antiderivative of g(x)
  (x 2)(x 3) ?
• A. (1/2 x 2 2x )(1/2 x 2 3x ) C
• B. 1/3 x 3 6x C
• C. 1
• D. 1/3 x 3 5/2 x 2 6x C
• E. 2x 5

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The Definite Integral (9/7/12)

• What does it mean to integrate a function over
  some part of its domain?
• That is, given a function f (x) defined on an
  interval a, b, what doesmean?
• How can we compute this number?

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The Fundamental Theorem

• Given a function f(x) on an interval a,b, the
  Fundamental Theorem of Calculus tells us how the
  definite integral (a number) and the
  antiderivative (a function) are related.
• Part 1 says you can get an antiderivative of f by
  turning the definite integral into a function of
  the right-hand endpoint. (This part is less used
  more theoretical.)
• Part 2 says that we can compute the definite
  integral provided we can find an antiderivative.
  Then we just evaluate that at the endpoints and
  subtract. (Used!)

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FTC - A Quick Outline

• Given a function f (x ) on a, b
  F (x ) an antiderivative of f
• Part 1 ? (by freeing up right endpoint)
• Part 2 ? (by evaluating F (b) F (a ) )

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Examples

• Example of Part 1Q What is an antiderivative
  of cos(x 2)?A
• Example of Part 2 (weve seen lots!)Q What is
  ?A arctan(6) arctan(2)

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Assignment for Monday

• Review as needed antiderivatives, definite
  integrals, and the Fundamental Theorem of
  Calculus.
• On Monday we will stop reviewing and move
  forward!
• Have a good weekend (but not too good!).