I made another Calculus fabric through spoonflower (http://www.spoonflower.com/fabric/1187406), because I was so excited about my first Calculus fabric. Well, the material arrived in the mail today! How exciting!!! I also got my design of balloons on orange chevrons, but I have to work on perfecting the chevrons and getting it how I like it. So fun to get fabric in the mail! :) Click the photos for a larger view. :)
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!