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Comparison Test for Improper Integrals
Worksheet
Grade Level
Calculus II
CAL2.49 Comparison Test for Improper Integrals
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Consider \(I=\int_0
1/2
\frac{1}{x
6/5
(1+\lvert\ln x\rvert)}\,dx\), with integrand \(f(x)\). Which option gives a valid direct comparison for the nonnegative integrand and the correct conclusion?
A
For \(0
11/10}\); since \(\int_0^\delta \frac{1}{x
11/10
}\,dx\) diverges, \(I\) diverges.
B
For \(0
11/10}\le f(x)\); since \(\int_0^\delta \frac{1}{x
11/10
}\,dx\) diverges, \(I\) diverges.
C
For \(0
D
For \(0
11/10}\le f(x)\); since \(\int_0^\delta \frac{1}{x
11/10
}\,dx\) diverges, \(I\) converges.
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