# Indefinite Integrals

# Indefinite Integrals: Prim and Improper Quiz

Think you’ve got your head wrapped around

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

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

diverges

Q.

Q. The function

*f*(*x*) is graphed below.The integral

converges for any choice of

*a*converges only if

*a*> 0converges only if

*a*≥ 1diverges

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)

(II)

(III)

(I)

(II)

(I) and (II)

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