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Indefinite Integrals

Indefinite Integrals

Example 1

Determine whether the integral converges or diverges. Indicate on a graph the region whose weighted area is given by the integral. If the integral converges, find its value.

Example 2

Determine whether the integral converges or diverges. Indicate on a graph the region whose weighted area is given by the integral. If the integral converges, find its value.

Example 3

Determine whether the integral converges or diverges. Indicate on a graph the region whose weighted area is given by the integral. If the integral converges, find its value.

Example 4

Determine whether the integral converges or diverges. Indicate on a graph the region whose weighted area is given by the integral. If the integral converges, find its value.

 for p > 1

Example 5

Determine whether the integral converges or diverges. Indicate on a graph the region whose weighted area is given by the integral. If the integral converges, find its value.

 for p < 1

Example 6

Determine whether each statement is true or false. Explain your answers.

If  does not exist, then

must diverge.

Example 7

If  does not exist, then

must converge.

Example 8

Determine whether the integral converges or diverges, and find its value if it converges.

Example 9

Determine whether the integral converges or diverges, and find its value if it converges.

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