Suppose I have this function where a = 0 and b = .5 not sure on the latex tags for that
and I let
this is the part where I get confused...
or solve for dx completely
If I do it at the step above and continue on to
and plug in the corresponding values my answers do not come out correctly
Memo to all members: It helps if you type all of the problem rather than just the bits of it you think are important. (The fact that important information is either overlooked or considered unimportant is often a major reason why people can't do the question they post). This saves time for everyone.
You aren't going to find an elementary antiderivative for that function... so unless you use estimation techniques or just put in into a calculator for the values of b=x that you want, I don't think you're going to get an answer
You could use taylor series to get as good an estimation as you'd like
You will have to use technology to evaluate I(x) for x = 0.5, 1, 1.5, 2. Was that made clear in the question?
Except for when x = 0 in which case obviously I(0) = 0.