Improper Integrals

• Feb 8th 2010, 05:09 PM
Belowzero78
Improper Integrals
1. Determine whether the improper integral converges or diverges.

integral(1/((abs(x-2))^(1/3)))dx
Lower limit: 20
Upper limit: 22

First i let u = x-2, so du=dx. and i calculated what u would be as a result of the substitution: when x=22, u=20, and when x=20, u =18. I'm not sure whether I have to split and do the integral separated into two terms.
• Feb 8th 2010, 05:23 PM
skeeter
Quote:

Originally Posted by Belowzero78
1. Determine whether the improper integral converges or diverges.

integral(1/((abs(x-2))^(1/3)))dx
Lower limit: 20
Upper limit: 22

First i let u = x-2, so du=dx. and i calculated what u would be as a result of the substitution: when x=22, u=20, and when x=20, u =18. I'm not sure whether I have to split and do the integral separated into two terms.

as you have it written, this is not an improper integral.

also, given the limits of integration, the absolute value is not needed either.

recheck the problem.
• Feb 8th 2010, 05:26 PM
Belowzero78
Yes it is.

It should be 1/(abs(x-21))^(1/3)

I.e. Cube root