6.2 Improper Integrals

Improper Integral where upper limits is NOT finite

Picture – Page 491 - Improper integrals as limits of proper integrals

Improper integrals may Converge or Diverge

Explore a couple of examples:

For the function

Examine the graph and finite limits to explore

The area under the curve to the right of 2 appears to approach ??

Consider a similar example:

What does the area appear to approach for this function??

The Improper Integral

If f(x) is continuous for x > a, then

If the limit exists, the improper integral is said to converge to the value of the limit. If the limit does not exist, the improper integral diverges.

Sometimes, it is useful to check by evaluating larger and larger values of N using the integration feature of the graphing calculator.

#12

#14

#16

A Useful Limit for Improper Integrals

For any power p and positive number k,

Assignment: 6.2 page 484 1-21 odd, 29, 31