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March 2, 2015

March 2, 2015

Posted by **Hannah** on Friday, October 22, 2010 at 8:34pm.

The integral from 0 to 7 of -1/((x-5)^2)dx

I keep getting 0.7 but apparently I am wrong.

- Calculus -
**Hannah**, Friday, October 22, 2010 at 9:11pmApparently it diverges to negative infinity. Can someone please explain to me why?

- Calculus -
**MathMate**, Friday, October 22, 2010 at 9:55pmI do not know how you got 0.7, negative infinity seems to me correct because there is an asymptote at x=5.

For improper integrals where the vertical asymptote is between the integration limites, we have to be careful not just evaluate the integral at the two limits.

Instead, we will subdivide the integral into two, from 0 to 5 and from 5 to 7.

If both integrals converge, then you have convergence and the integral is defined.

If there are more vertical asymptotes, you will need to subdivide accordingly.

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