What you did is correct.
Then you must compute
Let then
The integral becomes
Hi, new to this website. I am trying to teach myself integration out of a textbook and needs some help. The question is to find the area enclosed by the y axis, the curve y=1/(x^2) and the lines y=1 and y=4 in the first quadrant. I rearranged the equation to make x the subject {x= +or-sqrt(1/y)}, is that correct? Then, I don't know how to integrate +or-sqrt(1/y) to find the area between the limits of 4 and 1. If someone could explain this in beginners terms that is easy to follow I would greatly appreciate it. Thanks
In this case I think recognising and applying the usual rule is a lot simpler than making a substitution.
Note: There are many courses where integration and its mechanics are introduced but the technique of integration by substitution is not taught and a student would be required to deal with an integral like the one in this thread.