Why do you believe you should be able to do it?
Have you noticed the symmetry about x = 1? And the limited Domain, 0 <= x <= 2?
hello again,
I am trying to integrate this expression and I can't seem to be able to do so. I would greatly appreciate it if you can help me. The expression is: 1/(1 + sqr(2x - x^2)).
I tried multiplying the denominator with 1- sqr(2x - x^2) but to no avail. I then tried to rewrite the numerator as 1 - x + x, still stuck. I also tried to rewrite the denominator as (u - 2)/2, but I failed to find a solution. anyone any hint, please?
Wolfram Alpha's solution ...
integral of 1/(1+sqrt(2x-x^2)) dx - Wolfram|Alpha
TKHunny,
I believe I should be able to evaluate the integral because it was on a test in the past at the school I go.
skeeter,
that is the expression I arrived at, but did not have the idea of reforming it into a trig expression. I guess I will write x - 1 = sin (or perhaps cos), and see what I get.
Thank you all for your reply.
No good. It is or it isn't. As soon as the denominator was "rationalized", the Domain issue was introduced unless it can be show that there is no Domain issue. You might impress your teacher if you take a look at it.
You must answer this question: Are the first and last expressions equivalent? . If they are, then you're done. If they are not, what are you going to do about the transformation?
TKHunny, impress my teacher? I'd rather not before I get into wining and complaining about all the wrong at school, I'll just ask you or skeeter whether I integrated correctly 'the second' expression that skeeter derived. otherwise, I understand you perfectly well, TKHunny. You do have a point.
The substitutions I did are as follows: