renyikouniao
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Use the comparison test to find out whether or not the following improper integral exist(converge)?
integral(upper bound:infinity lower bound:2) 1/(1-x^2) dx
Here's my solution for 3),but I think something went wrong
For all x>=2
0<=-(2-2x)<=-(1-x^2) that means: 0<=-1/(1-x^2)<=-1/(2-2x)
and
integral (upper bound : infinity.lower bound : 2)
-1/(2-2x)=1/2lim(t->infinity)[In(2-2t)-In(-2)]
According to Comparison Test
If ) the integral -1/(2-2x) is convergent,then the integral -1/(1-x^2) is convergent.
But the integral -1/(2-2x) is divergent...so I don't know what to do next...
integral(upper bound:infinity lower bound:2) 1/(1-x^2) dx
Here's my solution for 3),but I think something went wrong
For all x>=2
0<=-(2-2x)<=-(1-x^2) that means: 0<=-1/(1-x^2)<=-1/(2-2x)
and
integral (upper bound : infinity.lower bound : 2)
-1/(2-2x)=1/2lim(t->infinity)[In(2-2t)-In(-2)]
According to Comparison Test
If ) the integral -1/(2-2x) is convergent,then the integral -1/(1-x^2) is convergent.
But the integral -1/(2-2x) is divergent...so I don't know what to do next...