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Math Help - Need some hints on this.

  1. #1
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    Need some hints on this.

    Need some hints on this.-screenshot.png


    I know for the first one it's area of a trapezoid, but it's in the negative region is that a problem?

    And Base one is -5 and base two I believe is -4 correct?

    And for the second one I think I have to add up all the areas, but what do I do for the parabola? Use Area of a semicircle formula?
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  2. #2
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    You are not given a equation for the parabola?

    Are you aware of the forums policy on giving answers to questions that could contribute to your final mark?
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  3. #3
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    I'm not asking for answers.

    I only ask about the bases, because I'm looking for some confirmation.

    I will be doing the final answers, I want to do the final answers. I don't want anyone to have the glory of finding the final answer but me.

    I just want to make sure that my methods are correct, that I'm heading in the right direction.

    If you'd like I'll just go on what I'm thinking and post if it didn't work.
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  4. #4
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    Quote Originally Posted by Zanderist View Post
    I'm not asking for answers.

    I only ask about the bases, because I'm looking for some confirmation.

    I will be doing the final answers, I want to do the final answers. I don't want anyone to have the glory of finding the final answer but me.

    I just want to make sure that my methods are correct, that I'm heading in the right direction.

    If you'd like I'll just go on what I'm thinking and post if it didn't work.
    Regarding question B, my opinion is that the problem is not well stated. We are given that the shaded region has area A. Then we are asked to estimate. But we should give the answer in terms of A and there should be no estimation.

    A tip: integral gives signed area.
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  5. #5
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    Part A: -8

    Just got it using the trapezoid formula.

    This now means that:

    \(\int_{-5}^0 f(x) dx =-8\)
    The other trapezoid is equal to the other one only it's positive 8


    \(\int_{5}^0 f(x) dx =8\)
    Now I just need to figure out


    \(\int_{5}^7 f(x) dx =\)
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  6. #6
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    Quote Originally Posted by Zanderist View Post
    Click image for larger version. 

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ID:	18957


    I know for the first one it's area of a trapezoid, but it's in the negative region is that a problem?
    It means that the integral is the negative of the area, not the area. Areas are never negative.

    And Base one is -5 and base two I believe is -4 correct?
    No, it is not. lengths are also never negative. The top base is 5 and the lower base is 3 not 4.

    And for the second one I think I have to add up all the areas, but what do I do for the parabola? Use Area of a semicircle formula?
    The problem says "estimate" and there can be many equally good estimates to such a value. I might suggest using, not the area of a semi-circle, but the area of a semi-ellipse. If an ellipse has semi-axis lengths of a and b, then its area is \pi ab and the area of half an ellipse is \frac{1}{2}\pi ab. The base across the parabola has length 2 so the semi-axis is 1. The depth of the parabola is 1 so that semi-axis is 1.

    However, on a closer look I see that the problem says "If the vertical red shaded area in the graph has area A" which makes me think you are supposed to give an answer in terms of "A", not actually find A. But then they wouldn't say "estimate" would they? I agree with undefined that B is not well defined.

    Caution- the parabola is also below the x-axis.

    Since -8+ 8= 0, I think it would be worth using one of your attempts to answer "-A"!
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