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Math Help - Help with a problem in maple

  1. #1
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    Help with a problem in maple

    I need help with following maple problem. All I need help with right now is finding the a and b in part a. If I have any problems later, I may be back for more help, but right now I just need help finding a and b. Anyway here is the problem:

    Let S be the solid obtained by revolving the region bounded between
    1
    u(x) = - x + 2
    2

    and
    1 2
    v(x) = 7 - - x + sin(x)
    5
    ; around the horizontal line
    y = -2
    .

    a. (4 points) Define functions u and v of x using the arrow notation. Find the x-values of the two points of intersection and give them the names a and b. Hint: a will be negative and b will be positive.
    >
    >

    b. (3 points) Plot your functions u and v together with a representative vertical rectangle. Include the axis of rotation (the line
    y = -2
    ) in your plot.
    >
    >

    c. (2 points) Use animatesor (using the option
    method = washers
    ) and plotsor to plot the solid of revolution. Use the option
    scaling = constrained
    in both commands.
    >
    >

    d. (3 points) Use integration to find the volume of the solid S correct to ten significant digits. (Your answer should be between 1000 and 1500 cubic units.)
    >
    >

    --------------------
    I am not sure how to get a and b in part a of the above problem. Do I plug in -2 into the equations and that will give me my a and b? Or do I need to solve something in maple to figure out what they are? Anyone know what I am supposed to do? I'm kind of lost. Thanks in advance to anyone who can help.
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  2. #2
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    I am not sure why my functions didn't show up correctly in my post, but they should be v(x) = 7-(1/5)*x^2+sin(x) and u(x) = (1/2)*x+2. Sorry about that.
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  3. #3
    Senior Member bkarpuz's Avatar
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    I really dont understant what you want, but I have some codes that can help you.

    Code:
    u:=x->x^2/2+1; #define the function 
    
    
    
    
    u
    Au:={solve(u(x)=1,x)}; #solve 
    
    
    
    
    u(x)=1 with respect to 
    
    
    
    
    x
    Bu:={solve(u(x)=2,x)}; #solve 
    
    
    
    
    u(x)=2 with respect to 
    
    
    
    
    x
    plot(u(x),x=Bu[2]..Bu[1]); #plot u by considering 
    
    
    
    
    -\sqrt{2}\leq x \leq\sqrt{2}
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  4. #4
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    I am wanting to know what the values of a and b values are for the functions v(x) = 7-(1/5)*x^2+sin(x) and u(x) = (1/2)*x+2 around the horizontal line y=-2. I have already defined v(x) and u(x) using arrow notation in a previous step and now just want the values for a and b, but can't figure out how to get them.Oh, and this problem is from a section called Volume: The Disk Method in my textbook, if that helps any. Usually a and b are just given to me, but in this problem they aren't and I can't figure out how to get them. Should I just plug -2 into the statements or should I do an fsolve or something to find the values of a and b. Thanks in advance to anyone who can help.
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