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Math Help - Area of region bounded by curves...where am I going wrong?

  1. #1
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    Area of region bounded by curves...where am I going wrong?

    The point of intersection for x would be 4 so my bounds would be 0 and 4 since the absolute value makes one bound 0. Then I subtract the two, sincd 2x is the upper It'd be 2x-(x^2-8) which becomes 2x-x^2+8 and after integration it would be 2x^2/2-x^3/x+8x. I plug in four and get 80/3 every time. Where am I going wrong?
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  2. #2
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    A certain function must be integrated for -4\le x\le4. Put f(x)=|2x|,\,g(x)=x^2-8 and note that f(x)\ge g(x) on [-4,4] and the integral is \int_{-4}^{4}{\big(\left| 2x \right|-x^{2}+8\big)\,dx}=2\int_{0}^{4}{\big(\left| 2x \right|-x^{2}+8\big)\,dx}=\frac{160}{3}.
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  3. #3
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    OK thanks but could you explain more clearly how you knew the first function was greater than the second on that interval?
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  4. #4
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    Graph it or just pick any number of the interval (not whose make the functions zero) and you'll see.
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