calculus 2 Comparison Test for Improper Integrals - Now that weve seen how to actually compute improper integrals we need to address one more topic

calculus 2 Comparison Test for Improper Integrals - Now...

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Comparison Test for Improper Integrals Now that we’ve seen how to actually compute improper integrals we need to address one more topic about them. Often we aren’t concerned with the actual value of these integrals. Instead we might only be interested in whether the integral is convergent or divergent. Also, there will be some integrals that we simply won’t be able to integrate and yet we would still like to know if they converge or diverge. To deal with this we’ve got a test for convergence or divergence that we can use to help us answer the question of convergence for an improper integral. We will give this test only for a sub-case of the infinite interval integral, however versions of the test exist for the other sub-cases of the infinite interval integrals as well as integrals with discontinuous integrands. Comparison Test If on the interval then, 1. If converges then so does . 2. If diverges then so does . Note that if you think in terms of area the Comparison Test makes a lot of sense. If is larger than then the area under must also be larger than the area under .
Example 1 Determine if the following integral is convergent or divergent.

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