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The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus: FTC (Yeah, You Know Me) Quiz Quiz

Think you’ve got your head wrapped around The Fundamental Theorem of Calculus? Put your knowledge to the test. Good luck — the Stickman is counting on you!
Q. The Fundamental Theorem of Calculus says that


 provided f = F' is continuous on [a,b]
 provided f = F' is continuous on [a,b]
 provided f = F' is continuous on [a,b]
 provided f' = F is continuous on [a,b]
Q.


0
10
Q. For what value(s) of a in [0,2π] is ?


π
π, 2π
0,2π
0,π,2π
Q.


b4b2
4x – 2x
4x – 42
b2 b4
Q. 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) only
(I) and (II)
(I) and (III)
(I), (II), and (III)
Q. If x is measured in meters and n(x) is measured in Newtons, what are the units of 


Newtons
meters
Newton-meters
Newtons per meter
Q. If x is measured in meters and n(x) is measured in Newtons, what are the units of


Newtons
meters
Newton-meters
Newtons per meter
Q. Find the average value of f(x) = 4 – x2 on [-1,2].


3
9
Q. 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.



0 meters per second
2.3 meters per second
17 meters per second
21.6 meters per second
Q. 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?



10 hours
11 hours
12 hours
13 hours
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