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Math Help - areas between curves

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    Exclamation areas between curves

    there is a line through the origin that divides the region bounded by the parabola y= 8x-2x^2 and the x-axis into two regions of equal area. What is the slope of the line?

    I can't figure it out. I don't know how to start
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  2. #2
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    Quote Originally Posted by zaddie21 View Post
    there is a line through the origin that divides the region bounded by the parabola y= 8x-2x^2 and the x-axis into two regions of equal area. What is the slope of the line?

    I can't figure it out. I don't know how to start
    calculate the area in quad I bounded by the parabola and the x-axis, call that area A.

    let the line be y = mx

    find the intersection of the line and parabola in quad I ...

    mx = 8x - 2x^2

    0 = (8-m)x - 2x^2

    0 = x(8 - m - 2x)

    x-values of intersection are x = 0 and x = \frac{8-m}{2}


    \frac{A}{2} = \int_0^{\frac{8-m}{2}} (8x-2x^2) - mx \, dx

    evaluate the integral and solve for m ... have fun with the algebra.
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