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Math Help - Confirmation of Right Answer of Area Between Curves

  1. #1
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    Confirmation of Right Answer of Area Between Curves

    Is the answer between curves of this equations
    y=2x-7
    y=x^2+4x-7 equal to 8/3 check please! thanks
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  2. #2
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    Hello, v3ndetta!

    I got a different answer . . .


    Is the area between the curves: . \begin{Bmatrix}y\:=\:2x-7 \\ y\:=\:x^2+4x-7\end{Bmatrix} . equal to \frac{8}{3} ?

    They intersect when: . 2x-7 \:=\:x^2+4x-7

    . . x^2+2x \:=\:0 \quad\Rightarrow\quad x(x+2)\:=\:0 \quad\Rightarrow\quad x \:=\:-2,\:0


    The line is above the parabola over this interval

    . . so we have: . A \;=\;\int^0_{-2}\bigg[(2x-7) - (x^2+4x-7)\bigg]\,dx \;=\;\int^{\,0}_{\text{-}2}(-x^2-2x)\,dx

    . . = \;-\frac{x^3}{3} - x^2\,\bigg]^0_{-2} \;=\;(0 - 0) - \left(\tfrac{8}{3} - 4\right) \;=\;-\left(-\tfrac{4}{3}\right) \;=\;\boxed{\frac{4}{3}}

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  3. #3
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    thanks very much! lifesaver
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