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Finite and Infinite Areas Exercises

Example 1

Look at the picture below, which shows a region A within a region B.

If the area of region A is infinite, what does that tell us about the area of region B?

Example 2

Look at the picture below, which shows a region A within a region B.

If the area of region B is finite, what does that tell us about the area of region A?

Example 3

Look at the picture below, which shows a region A within a region B.

If the area of region A is finite, what does that tell us about the area of region B?

Example 4

Look at the picture below, which shows a region A within a region B.

If the area of region B is infinite, what does that tell us about the area of region A?

Example 5

From the graph below, determine if each integral converges, diverges, or if its behavior cannot be determined.

(a)

(b)

(c)

(d)

(e)

(f)

Example 6

From the graph below, determine if each integral converges, diverges, or if its behavior cannot be determined.

(a)

(b)

(c)

(d)

(e)

(f)

Example 7

From the graph below, determine if each integral converges, diverges, or if its behavior cannot be determined.

(a)

(b)

(c)

(d)

(e)

(f)

Example 8

If 0 < f (x) and

converges, does

converge or diverge?

Example 9

Use the graph to determine if  converges or diverges.

Example 10

Does  converge or diverge?