## anonymous one year ago I'm stuck... (integral in graph form)

1. anonymous

2. ganeshie8

Hint : $\int_0^1 \frac{1}{x^n}\, dx$ converges when $$n\lt 1$$ and diverges when $$n\ge 1$$

3. ganeshie8

|dw:1436018433814:dw|

4. anonymous

5. anonymous

Actually wouldn't all the graphs converge because they are all from the intervals of 0 to 1?

6. ganeshie8

we don't know about red graph as the area below that red graph is greater than the area below blue graph

7. 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]

8. 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.

9. anonymous

Oh whoops, thanks!