Stanley Munoz
04/10/2023 · Senior High School
Let \( f(x)=x-2, g(x)=-x \), and \( h(x)=4+2 x-x^{2} \) then (i) Sketch the graphs of \( f, g \) and \( h \) on the same system of axes. (ii) Find the area of the region above the two functions \( f(x)=x-2 \) and \( g(x)=-x \) and below the third funciton \( h(x)=4+2 x-x^{2} \).
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The area of the region above the functions \( f(x)=x-2 \) and \( g(x)=-x \) and below the function \( h(x)=4+2x-x^2 \) is calculated by integrating the difference between the functions over the interval from -2 to 1. The final result of the integration gives the area.
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