The initial problem is: http://www.wolframalpha.com/input/?i=integrate(sqrt(x^2+-+1)%2Fx%2C+x%2C1%2C2)
My problem is not in the substitution part but rather on the limits of integration. I tried "an easy way out" which is to just use => instead of = signs and not put limits of integration and then just turn the variables into x variables (initial variables) and use the initial limits of integration but the problem I am having is from this step:
integral of (tan^2 (theta) (dtheta)) = tan(theta) - (theta) + C = sqrt(x^2 - 1) - arcsec(x) and when I try to find the value for the final answer:
sqrt(2^2 - 1) - arcsec(2) - 0 + arcsec(1)
both bold parts give me errors on the calculator which means they do not exist. I do recall that theta should be between [0, pi/2) or [pi, 3pi/2) but there is a final answer in the back of the book (sqrt(3) - pi/3)which suggests I am doing something wrong.
Any help would be GREATLY appreciated!
Thanks in advance!
I had tried arcsec(2) = 1/arccos(2) and arcsec(1) = 1/arccos(1). So, what I have to do instead is take the reciprocal of the fraction and then use the reciprocal trig?
By this I mean, on the first example, arcsec(2) = arcsec(2/1) = arccos(1/2) ?
and for the second;
arcsec(1/1) = arccos(1/1) ?