Calc Example: For When You Hit sqrt(2-2cos(t)) And Need To Integrate!April 19, 2012 at 1:08 am | Posted in Calculus, Calculus Example, College, integrals, integrate sqrt(2-2cos(t)), integration, Jon Rogawski, Kristin Bell, math, Mathematics, University, vector calculus, vectors | Leave a comment
This example almost made my brain explode! I didn’t know about the Weierstrass substitution method (see this link for more info.: http://en.wikipedia.org/wiki/Weierstrass_substitution) when I began this problem…which is what I needed to complete the problem. I’m still unsure if I did it correctly, because we were supposed to find the integral over 0 to 2*pi, but the integration method only works over 0 to pi, so I ended up multiplying the answer by 2 (because 2 times pi is 2*pi) which got me the answer the book was asking for, but it seemed odd to do it that way. The question is number 18, section 13.3 from the Jon Rogawski Calc book in case you are interested. I think it is a pretty great textbook by the way…I mean as far as math textbooks go! We were also supposed to find when the speed was at its max, but I was so tired I just figured it was at pi and gave up! So, here’s the problem!