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Indefinite Integrals

Indefinite Integrals

Indefinite Integrals: Prim and Improper True or False

1. An "improper integral" isanother name for an indefinite integral.
2. 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 II and IV

3. The integral diverges
4. If  then the integral is a definite integral
5. Which of the following integrals must converge?
6. The integral diverges
8. The function f ( x ) is graphed below.

The integral

converges only if a ≥ 1

9. To determine if

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

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

(III) (I)