Determine whether or not the following intervals converge,showing your reasoning
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The first one can be compared to a Riemann integral :
You can also remember that an antiderivative of is .
Which also diverges.
An antiderivative for is arctan function.
Edit : 5th post ^^
For the second one observe that hence the integral converges by direct comparison.
Originally Posted by Krizalid For the second one observe that hence the integral converges by direct comparison. You need to be careful here. You should actually say, .
You need the part, I am sure you can see why.
Or a stronger way to say this is, .
In general if and the integral of converges then integral will converge also.
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