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Thread: Help computing the area of a region bounded by the graphs of two function.

  1. #1
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    Help computing the area of a region bounded by the graphs of two function.

    Question as is

    Compute the area of the finite region bounded by the graphs of the functions

    y=2x2 , and y=-2x2-8x+32

    So i first set them equal to each other to find my points.

    2x2=-2x2-8x+32

    -4x2-8x+32=0

    -4(x+4)(x-2)=0
    x=-4, x=2

    so when I integrate it will be from the limit of -4 to 2 right?

    this is where I get stuck.
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  2. #2
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    Re: Help computing the area of a region bounded by the graphs of two function.

    $f_1(x) = 2x^2$

    $f_2(x) = -2x^2 - 8x + 32$

    $f_2(x) \geq f_1(x),~\forall x\in[-4,2]$

    $\begin{align*}
    \displaystyle

    &\phantom{=}\int_{-4}^2~f_2(x)-f_1(x)~dx \\ \\
    &= \int_{-4}^2~-2x^2 - 8x + 32- 2x^2~dx \\ \\
    &= \int_{-4}^2~-4x^2 - 8x + 32~dx \\ \\
    &= \left . -\dfrac 4 3 x^3 - 4x^2 + 32x \right |_{-4}^2 \\ \\
    &=144

    \end{align*}$
    Thanks from XxXScorpionXxX
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  3. #3
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    Re: Help computing the area of a region bounded by the graphs of two function.

    thanks again.
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