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Math Help - comparison theroem

  1. #1
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    comparison theroem

    Hi the instructions are to use the comparison thereom to determine whether the following integral is convergent or divergent

    integral sign (S) sqrt x/(x^3 +1) dx

    I am running into a mental road block and can't figure out how to get rid of the sq rt x as the numerator

    What do I need to do to simplify this integral?

    Thanks

    Struggling calculus beginner
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  2. #2
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    Krizalid's Avatar
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    i see no bounds, but well.

    i'll presume that is 0\le x<\infty or 1\le x<\infty.

    suppose is the first case, the split the integral into two pieces, one goes for [0,1] and let's analyze the second piece for x\ge1, then \frac{\sqrt{x}}{x^{3}+1}<\frac{\sqrt{x}}{x^{3}}=\f  rac{1}{x^{5/4}}, hence the integral converges.
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  3. #3
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    Sorry about my oversight

    it is S a= 1 and b= infinity

    so I assume that what you did is complete and I don't have to worry about the 0 to 1 section? right

    Thanks

    Calculus beginner
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  4. #4
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    Krizalid's Avatar
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    sure, since the function is integrable there 'cause is continuous on that compact set.
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