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. Let
For what values of x does F(x) = 0?
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_1.png)
x = 0
x = 2πk where k is any integer
x = πk where k is any integer
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_2.png)
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_3.png)
Q. Let
. For which values of x is F(x) positive?
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_4.png)
x > 0
x > 1
|x| > 1
|x| < 1
Q. Define a function F(x) by
Which of the following best represents the value F(π)?
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_graphik_1.png)
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_graphik_2.png)
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_graphik_3.png)
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_graphik_4.png)
Q. Let f(x) be a continuous function. The second Fundamental Theorem of Calculus says that
the function
is an antiderivative of f(x).
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_6.png)
the function
is an antiderivative of f(x).
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_7.png)
the function
is an antiderivative of f(x).
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_8.png)
the function
is an antiderivative of f(x).
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_9.png)
Q. Which of the following is NOT an antiderivative of eex?
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_10.png)
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_11.png)
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_12.png)
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_13.png)
Q. Which of the following is an antiderivative of cos (x2) that equals 2 when x = π?
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_14.png)
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_15.png)
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_16.png)
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_17.png)
Q. Let
and
. Then
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_18.png)
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_19.png)
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_20.png)
0
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_21.png)
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_22.png)
f(b) – f(a)
Q. The equation
means
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_23.png)
F is an antiderivative of f.
f is an antiderivative of F.
F is the derivative of f.
f '(x) = F(x).
Q.
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_24.png)
cos (x2)
-cos (x2)
cos(x2) – cos 4
2 – cos(x2)
Q.
![](https://media1.shmoop.com/images/calculus/calc_ftoc_quiz_3_latek_25.png)
ex6
ex6 × 3x2
ex6 · 3x2
e(3x2)2