9 Attachment(s)

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.

Attachment 24638

These are the instructions for the problem.

Attachment 24639

This is the problem #7.

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Finding the points of integration.

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My graph, replica from my graphing calculator.

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Teachers version of equation and answer.

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Me working through first integration of teachers equation.

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Working through the second integration of teachers equation.

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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.

Re: Integration, problem from our area between two curves segment. Calculus II

Which question are you actually trying to do?

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.