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Home Infinite Series Series With Positive Terms Examples Example 8: Integral Test  
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Example 8: Integral Test
Use the Integral Test to test the improper integral for convergence. By Example 7 the series converges. For x > 1 the function f(x) = (ln x)/x^{2} is continuous, positive, and has derivative f'(x) = x^{3}(1  2 ln x). Thus for x > √e >, f'(x) < 0 and f(x) is decreasing. Therefore the Integral Test applies and the improper integral converges.


Home Infinite Series Series With Positive Terms Examples Example 8: Integral Test 