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Math Help - Areas and Differentials

  1. #1
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    Exclamation Areas and Differentials

    Hey guys I'm having problems on these three word problems. These problems are going to on a test with in two days. So here they are.

    17) Find the area under the "curve" y=3 from x=1 to x=3

    18) Find the area between the curves y=x^2 and y=3x

    19) Solve the simple differential equation when dy/dx=3x^2 , x=2 , when y=3

    So these are the word problems.
    Thanks for the help.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Ok here we go

    Quote Originally Posted by uniquereason81 View Post
    Hey guys I'm having problems on these three word problems. These problems are going to on a test with in two days. So here they are.

    17) Find the area under the "curve" y=3 from x=1 to x=3

    18) Find the area between the curves y=x^2 and y=3x

    19) Solve the simple differential equation when dy/dx=3x^2 , x=2 , when y=3

    So these are the word problems.
    Thanks for the help.


    17) area under a curve is given by an integral...therefore the area from 1 to 3 of y=3 is given by \int_1^3{3}dx=6

    18)the area bounded by the two curves takes place between the curves intersections y=x^2,y=3x intersect at x=0,x=3...thefore since y=3x>x^2,{\forall{x}\in[0,3]} the area between the curves is given by \int_0^3{3x-x^2}dx
    19) \frac{dy}{dx}=3x^2...this is an SDE...so seperate to get dy=3x^2{dx}...integrate to get that y=x^3+C
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  3. #3
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    is it possible for you to explain a little more im still confuse. Thanks
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  4. #4
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    Hello,

    The "area under a curve" corresponds to the integral of the function.

    More precisely :

    The integral of a function between a and b corresponds to the area limited by the curve of the fuction, the x-axis and the lines x=a and x=b.



    Here is an example.

    For the second question, i think you need to know that :

    \int_a^b f(x)dx - \int_a^b g(x)dx=\int_a^b (f(x)-g(x))dx
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  5. #5
    MHF Contributor Mathstud28's Avatar
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    Ok

    First off I am assuming you understand integrals... \lim_{n \to {\infty}}\sum_{n=0}^{\infty}f(M_{i})\cdot{\Delta{x  }}=\int_a^b{f(x)}dx...where \Delta{x}\frac{b-a}{n}...if so then of find area to a point...if so apply the fact that f(x) is the curve...and a and b are the limits of integration to part a...for part b you must apply the integral concept except you are looking for the area between where two curves intersect...once you have found these intersections they will be your limits of integration and your f(x) will be your curve that is greater on that interval minus your curve that is less on that interval...
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  6. #6
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    So using this formula i should do good on the test.Thanks
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