anonymous
  • anonymous
I'm stuck... (integral in graph form)
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
ganeshie8
  • ganeshie8
Hint : \[\int_0^1 \frac{1}{x^n}\, dx\] converges when \(n\lt 1\) and diverges when \(n\ge 1\)
ganeshie8
  • ganeshie8
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anonymous
  • anonymous
What about the other functions?
anonymous
  • anonymous
Actually wouldn't all the graphs converge because they are all from the intervals of 0 to 1?
ganeshie8
  • ganeshie8
we don't know about red graph as the area below that red graph is greater than the area below blue graph
ganeshie8
  • ganeshie8
green graph integral must converge as the area under green curve is less than the area under blue curve in the interval [0,1]
UsukiDoll
  • UsukiDoll
That was the p-test and it depended on the exponent's value. If it's greater than 1 then it diverges. If it's less than 1, then it converges. It appears that the graph in blue is the original equation and graph transformations occurred for green and red.
anonymous
  • anonymous
Oh whoops, thanks!

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