There way is correct, and so is mine.
When we integrate
, we still need to apply a substitution.
The integral would become
What they did was re-substitute u back into the antiderivative:
, and then they evaluated from 1 to 2.
However, the way I did it, I eliminated the need to re-substitute u back into the equation.
I did this when I converted the integration limits.
Since
and the x limits of integration were from 1 to 2, I saw that the u limits would be from
to
So when you evaluate, we see that
I hope this clarified things! If you have questions, feel free to ask. We're here to help you!
--Chris