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The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus: Did Isaac Newton Enjoy Figs? 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. Let 


x = 0
x = 2πk where k is any integer
x = πk where k is any integer
 and , where k is any integer.
Q. Let . For which values of x is F(t) positive?


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)?



Q. Let f(x) be a continuous function. The second Fundamental Theorem of Calculus says that


the function is an antiderivative of f(x).
the function  is an antiderivative of f(x).
the function  is an antiderivative of f(x).
the function  is an antiderivative of f(x).
Q. Which of the following is NOT an antiderivative of eex?


Q. Which of the following is an antiderivative of cos (x2) that equals 2 when x = π?


Q. Let  and . Then 


0
f(b) – f(a)
Q. The equation means


F is an antiderivative of f.
f is an antiderivative of F.
F is the derivative of f.
f '(x) = F(x).
Q.


cos (x2)
-cos (x2)
cos(x2) – cos 4
2 – cos(x2)
Q.


ex6
ex6 × 3x2
e<sup>x6</sup> × 3x2
e(3x2)2
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