Integral and exponentials - XP Math - Forums

 XP Math - Forums Integral and exponentials

 06-14-2007 #1 YvesBenoit Guest   Posts: n/a Integral and exponentials I'm working on a 19 page assignment for my calculus course. Unfortunately this is a distance course, and there aren't many places I can go to for help... so bre with me. Question #1 (integral) (2 + 3cosx + (sinx)^3) / ((sinx)^2) dx $\int\frac{2 + 3cosx + (sinx)^3}{(sinx)^2} dx$ Developing... ((integral) (2/(sinx)^2) + (3cosx)/((sinx)^2) + sinx) dx Might want to write that out before attempting since it's a little difficult to read it properly when typed out. Note that (sinx)^3 should usually be written out (sin^3)x. Question #2 (1/4)^x * 16^(x/2) The answer, I believe, is 1. However I can't seem to reach this by applying exponential laws. Last edited by Mr. Hui; 06-14-2007 at 05:04 PM..
 06-15-2007 #2 YvesBenoit Guest   Posts: n/a Ok I worked at the first problem and figured it out. using the identity 1/sinx = cscx... (2/(sinx)^2)x = 2(csc^2)x Using the identity cosx/sinx = cotx 3cosx/((sinx)^2) = 3cotx/sinx And using the identity 1/sinx = cscx 3cotx/sinx = 3cscxcotx Giving a final developed equation of (integral) (2(csc^2)x + 3cscxcotx + sinx) dx Remembering these derivatives cosx = -sinx cscx = -cscxcotx tanx = (csc^2)x Final integrated answer = -2cotx - 3cscx - cosx + C C being any integer. But I still can't figure out the second one, although it's probably much easier
 06-15-2007 #3 Mr. Hui     Join Date: Mar 2005 Posts: 10,609 Is the second problem an equation? __________________ Do Math and you can do Anything!
 06-15-2007 #4 YvesBenoit Guest   Posts: n/a Sorry, yes the 2nd was an equation. I played around with it and seem to have figured it out as well. f(x) = (1/4)^x * 16^(x/2) (1^x / 4^x) * 16^(x/2) 1^x = 1 so f(x) = 1/(4^x) * 16^(x/2) = 16^(x/2) / (4^x) = (sqrt16)^x / (4^x) = 4^x / 4^x = 1 I know I know... ended up figuring it by myself. However I did end up wasting hours while trying to figure it out.

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