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

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!*

**The Fundamental Theorem of Calculus***f*=

*F*' is continuous on [

*a*,

*b*]

*f*=

*F*' is continuous on [

*a*,

*b*]

*f*=

*F*' is continuous on [

*a*,

*b*]

*f*' =

*F*is continuous on [

*a*,

*b*]

*a*in [0, 2π] is ?

*b*

^{4}–

*b*

^{2}

*– 2*

^{x}

^{x}*– 4*

^{x}^{2}

*b*

^{2 }–

*b*

^{4}

*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.

*x*is measured in meters and

*n*(

*x*) is measured in Newtons, what are the units of

*x*is measured in meters and

*n*(

*x*) is measured in Newtons, what are the units of

*f*(

*x*) = 4 –

*x*

^{2}on [-1, 2].

*t*seconds after being thrown is given by the formula

*v*(*t*) = 9.8*t* + *v*_{0}.

Find *v*_{0} given that the ball travels 51 meters during the first 3 seconds after it is thrown.

*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?