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Math Help - Finding the area of a function and graph?

  1. #1
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    Finding the area of a function and graph?

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  2. #2
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    Quote Originally Posted by Da Freak View Post
    Okay, what have you done? Have you graphed the function?

    Also there is a lack of information. The region enclosed by y= x^2+ x, x= 0, and x= 2 is not bounded and does not have a finite area. You are missing one boundary. Is y= 0 also a boundary line?


    If so, to do this you only need to know:
    1) The area is \int_0^2 f(x)- g(x) dx where f(x) and g(x) are the equations of the upper and lower boundaries, respectively. (And, here, g(x)= 0.)

    2) The anti-derivative of x^n is \frac{1}{n+1}x^{n+1}.
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  3. #3
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    <BEGIN SPOILER>








    You need to find definite integral of x^2+x, which gives \int_0^2{(x^2+x)dx} = (\frac{1}{3}x^3 + \frac{1}{2}x^2)[2] -  (\frac{1}{3}x^3 + \frac{1}{2}x^2)[0]

    You can finish up

    </SPOILER>
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  4. #4
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    well sketch the graph first of all. complete the square and you can see that its just a shifted parabola. now they want you to find the area enclosed by the graph and the vertical lines x=0 and x=2. i also assume y=0 is a boundary otherwise the area would not be finite. draw a rectangle in the region with height f(x) and width dx. the area of that rectangle would be (x^2 + x)dx so when you sum up a lot of those rectangles and take the limit as the width of those rectangles go to zero, you get the integral from 0 to 2 of (x^2 + x)dx. that is an easy integral to compute and you can complete the problem from there.
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