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# 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

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***The Fundamental Theorem of Calculus**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.

*b*

^{4}–

*b*

^{2}

4

*– 2*^{x}^{x}4

*– 4*^{x}^{2}*b*

^{2 }–

*b*

^{4}

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 ofNewtons

meters

Newton-meters

Newtons per meter

Q. If

*x*is measured in meters and*n*(*x*) is measured in Newtons, what are the units ofNewtons

meters

Newton-meters

Newtons per meter

Q. Find the average value of

*f*(*x*) = 4 –*x*^{2}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 + *v*_{0}.

Find *v*_{0} 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 + 2*t*

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