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Indefinite Integrals

Indefinite Integrals

Indefinite Integrals: Prim and Improper Quiz

Think you’ve got your head wrapped around Indefinite Integrals? Put your knowledge to the test. Good luck — the Stickman is counting on you!
Q. An "improper integral" is

another name for an indefinite integral.
a limit of definite integrals.
a limit of indefinite integrals.
an integral that can't be evaluated by substitution.
Q. Which of the following statements must be true? Assume f is continuous and well-behaved on (0,∞).

(I) If  then  converges.
(II) If  then  diverges.
(III) If  diverges then 
(IV) If  converges then 

I and IV
II and III
I and III
II and IV
Q. The integral 

converges to 1
converges to 
converges to e
Q. If  then the integral

is a definite integral
is an improper integral and diverges
is an improper integral and converges
is an improper integral and may either diverge or converge.
Q. Which of the following integrals must converge?

Q. The integral 

converges to 0
converges to 1
converges to some unknown value

Q. The function f ( x ) is graphed below.

The integral

converges for any choice of a
converges only if a > 0
converges only if a ≥ 1
Q. To determine if

converges or diverges, it would be useful to compare the integrand to

Q. Given the graph below, which of the following integrals must converge?


(I) and (II)
(I), (II), and (III)