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Math Help - Integration, problem from our area between two curves segment. Calculus II

  1. #1
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    Integration, problem from our area between two curves segment. Calculus II

    I worked on this homework problem, went to class and when the teacher went over it he got a different answer than I did and set his equation up differently. I erased my work and started over, but the way he set up his equation didn't make sense to me and when I worked through it I got negative areas. I don't remember my initial process since I erased it to follow my teachers instruction but I believe I initially got 1/25, which I'm not sure is right either but when I use his version I get -9/5 and he expects 3/5 from it. I'm including pictures of the assignment, my initial footwork, and my graph, along with the equation and answer I copied off the board to day and the way I worked it out. Any help seeing why his version works and/or how it turns out to 3/5 or just where I can look at where I might have gone wrong would be an extra help. This was actually due today but he gave the class an extension until first thing in the AM. So I need to figure this out ASAP. Thanks in advance for any help.



    Integration, problem from our area between two curves segment. Calculus II-img_20120829_195748.jpg
    These are the instructions for the problem.
    Integration, problem from our area between two curves segment. Calculus II-img_20120829_195806.jpg
    This is the problem #7.
    Integration, problem from our area between two curves segment. Calculus II-img_20120829_195834.jpg
    Finding the points of integration.
    Integration, problem from our area between two curves segment. Calculus II-img_20120829_195848.jpg
    My graph, replica from my graphing calculator.
    Integration, problem from our area between two curves segment. Calculus II-img_20120829_195903.jpg
    Teachers version of equation and answer.
    Integration, problem from our area between two curves segment. Calculus II-img_20120829_195927.jpg
    Me working through first integration of teachers equation.
    Integration, problem from our area between two curves segment. Calculus II-img_20120829_195952.jpg
    Working through the second integration of teachers equation.
    Integration, problem from our area between two curves segment. Calculus II-img_20120829_200007.jpg
    Adding the results from the integrations.

    I've never posted pictures on here and when I wrote out my work I wasn't expecting to post it online so I hope you can read and see everything I'll check once it posts to see if it works.
    Attached Thumbnails Attached Thumbnails Integration, problem from our area between two curves segment. Calculus II-img_20120829_195748.jpg  
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  2. #2
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    Re: Integration, problem from our area between two curves segment. Calculus II

    Which question are you actually trying to do?
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  3. #3
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    Re: Integration, problem from our area between two curves segment. Calculus II

    I was trying to solve question number 7 which I stated under the picture. Essentially I need to find the area bounded by the equations y=x, y= 4x, and y=-x+2. My answer which I believe was 1/25 did not jive with my professors 3/5 so I erased my work to start over and use the equation set up the way he said to do it. When I solve it the way he set it up I get a negative answer (-9/5) that is not what he stated as the correct answer (3/5). I need to know if I'm solving his equation wrong or if the way he set up his equation is wrong.
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