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Math Help - question about area/perimeter/volume using integrals

  1. #1
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    question about area/perimeter/volume using integrals

    AP CALC AB problem (high school)

    1)
    f(x) = e^(-x/4) + sin (x^2), g(x) = (1/3)x^2 - x, and x-axis supposedly create a region where I am to find the area/perimeter/volume. When I graph this, there is no region such that satisfies the condition of all 3. Am I graphing this incorrectly? or is this AP calculus AB question just poorly/incorrectly written?

    2)
    g(x) = (5 e^(-x/6) ) (sin ((x^2) / 6)) and the x-axis enclose a region R. Again, I'm supposed to find area/perimeter/volume.

    I am pretty sure the region R enclosed by g(x) and the x-axis is infinite as it goes on and on and on...which would set up an infinite amounts of integral [x1,x2] + integral [x2,x3] + etc as the upper and lower bounds keep alternating due to the sin wave of the function.
    plot (5e^(-x/6))(sin((x^2)&#4 7;6)) - Wolfram|Alpha

    no domain was specified. I doubt the teacher meant to trick high school students with this. Am I looking at these two questions wrong? Thanks!
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  2. #2
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    Re: question about area/perimeter/volume using integrals

    Dude, you'll make more people interested of this post if you use latex to display your functions/formulas etc. :-)
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  3. #3
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    Re: question about area/perimeter/volume using integrals

    I see two separate regions. One section begins where (1/3)x^2 - x= e^{-x/4}+ sin(x^2) and ends where e^{-x/4}+ sin(x^2)= 0. The second region begins where that function is 0 again, then ends where (1/3)x^2 - x= e^{-x/4}+ sin(x^2).
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  4. #4
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    Re: question about area/perimeter/volume using integrals

    Quote Originally Posted by liquidFuzz View Post
    Dude, you'll make more people interested of this post if you use latex to display your functions/formulas etc. :-)
    I had already typed the formula out so I copy/pasted without even considering it. I probably should have went the extra effort :P

    Quote Originally Posted by HallsofIvy View Post
    I see two separate regions. One section begins where (1/3)x^2 - x= e^{-x/4}+ sin(x^2) and ends where e^{-x/4}+ sin(x^2)= 0. The second region begins where that function is 0 again, then ends where (1/3)x^2 - x= e^{-x/4}+ sin(x^2).
    I see the two regions as one unless you are considering the area between e^{-x/4}+ sin(x^2) and x axis. The two regions within the two domains you mention don't seem to cross on my graph, so I consider that as just 1 bound region. I do see 2 other regions bound by f(x) and g(x) but not x-axis.

    After much zooming in and out, I did finally find a very small region where x is approximately 3.1 and 2 larger regions to the right of it where x is approximately 3.5. This entire setup though seems incredibly unintuitive.

    However, I am more interested in the second setup with the infinite bound regions. I am pretty sure I am graphing it correctly. I just wouldn't know how to setup, for example, an area formula using integrals for an infinite number of regions without some complex sigma notation.
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