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Math Help - find the area of the region bounded by the graphs of the equations.

  1. #1
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    find the area of the region bounded by the graphs of the equations.

    i know how the function looks like when graphed because i used a graphing calculator... but what does y=0 mean???
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  2. #2
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    Re: find the area of the region bounded by the graphs of the equations.

    Hey asilvester635.

    Setting y = 0 means that you are finding the solutions of when the function crosses the x-axis.

    This is also known as finding the roots of the equation where f(x) = -x^2 + 3x = 0.

    Finding roots to equations has many purposes.
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    Re: find the area of the region bounded by the graphs of the equations.

    how do i solve this??? like how do i find the area?? how do i go about solving this equation?
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    Re: find the area of the region bounded by the graphs of the equations.

    Start by factorizing the equation into (x-a)(x-b) = 0 and then use the fact that x = a and x = b are solutions to this equation since at least one term has to be 0 in order for the LHS to be zero.
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    Re: find the area of the region bounded by the graphs of the equations.

    i don't get it....
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    Re: find the area of the region bounded by the graphs of the equations.

    Take the integral bounded at the intersection points.
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    Re: find the area of the region bounded by the graphs of the equations.

    y = 0 is the x-axis

    so, you're looking for the area between the curve y = 3x-x^2 and the x-axis

    note the curve intersects the x-axis when 3x-x^2 = 0

    x(3-x) = 0

    ... the zeros, x = 0 and x = 3 are the limits of integration.
    Thanks from asilvester635
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    Re: find the area of the region bounded by the graphs of the equations.

    thank you so MUCH!!!!!
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    Re: find the area of the region bounded by the graphs of the equations.

    so do i just straight up integrate the function? and then plug in the 3 and 0 into x?
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    Re: find the area of the region bounded by the graphs of the equations.

    \int\limits_a^b f(x) dx = F(b)-F(a)
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