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# Indefinite Integrals

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# Finite and Infinite Areas Exercises

### Example 1

Exercise. 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

Exercise. 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

Exercise. 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

Exercise. 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?