- #1
Rono
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Homework Statement
Determine if the following integrals are convergent or divergent. Explain why.
[itex]\int^{1}_{0} \frac{1}{1-x^{4}} dx[/itex]
The Attempt at a Solution
I've tried using Comparison Test, using [itex]f(x) = \frac{1}{1-x^{4}} and\; g(x) = \frac{1}{1-x}[/itex], [itex]0 \leq f(x)\leq g(x)[/itex] [itex]in ] 0,1 [ [/itex] and I know [itex]g(x)[/itex] is divergent. My question is if its plausible that, by using Comparison Test, if [itex]g(x)[/itex] is divergent, will [itex]f(x)[/itex] be divergent too?