Using integration to find limits

[waealu]

Homework Statement

The problem asks to integrate dx\(sqrt(abs(x-1))) from 0 to 2.
[itex]\int(dx/(sqrt(abs(x-1))))[/itex]

Homework Equations

I had the limit as b approaches 1 of the integral (from 0 to b) plus the limit as c approaches 1 of the integral (from c to 2).

The Attempt at a Solution

After integrating, I got 2(sqrt(x-1)). Then I plugged in my bounds for the two limit equations and got (0-2)+(2-0)=0. However, I know the answer is 4. What am I missing? I have a feeling that I am forgetting to do something with the absolute value.

 

[Dick]

Homework Statement

The problem asks to integrate dx\(sqrt(abs(x-1))) from 0 to 2.
[itex]\int\frac{}{}dx[/itex]

Homework Equations

I had the limit as b approaches 1 of the integral (from 0 to b) plus the limit as c approaches 1 of the integral (from c to 2).

The Attempt at a Solution

After integrating, I got 2(sqrt(x-1)). Then I plugged in my bounds for the two limit equations and got (0-2)+(2-0)=0. However, I know the answer is 4. What am I missing? I have a feeling that I am forgetting to do something with the absolute value.

You are forgetting to do something with the absolute value. You can't just integrate pretending it isn't there. |x-1|=x-1 on the interval [1,2] and |x-1|=1-x on the interval [0,1]. Integrate over the two intervals separately and add them.

 

[FieldDuck]

Er Dirk beat me to it.

 

[waealu]

Okay, thanks. I figured it out now.