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The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus: FTC (Yeah, You Know Me) True or False

1. The Fundamental Theorem of Calculus says that ->  provided f = F ' is continuous on [a, b]
2. -> 0
3. For what value(s) of a in [0, 2π] is ? -> 0, π, 2π
4. -> 4x – 2x
5. Let f be continuous on [a, b]. If F(x) and G(x) are antiderivatives of f, which of the following statements must be true?

(I)

(II) 

(III) If F(b) – F(a) = G(b) – G(a) then F and G must be the same function. -> (I) and (III)

6. If x is measured in meters and n(x) is measured in Newtons, what are the units of  -> Newtons per meter
7. If x is measured in meters and n(x) is measured in Newtons, what are the units of -> meters
8. Find the average value of f(x) = 4 – x2 on [-1, 2]. -> 3
9. A ball is thrown from a tall building. Its speed in meters per second t seconds after being thrown is given by the formula

v(t) = 9.8t + v0.

Find v0 given that the ball travels 51 meters during the first 3 seconds after it is thrown. -> 21.6 meters per second

10. Brianna leaves her cabin in the wilderness and drives towards civilization. Her velocity in miles per hour is

v(t) = 40 + 2t

where t is the number of hours since she left her cabin. To the nearest hour, how long does it take her to drive 600 miles? -> 12 hours


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