Question

What is the area of the shaded region on the graph shown?

Answer 1

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Answer 27/2

Explanation:

`f(x)=-x^3+5x\\F(x)=-(x^4)/(4) +(5x^2)/(2) \\F(2)=(-16)/(4)+(20)/(2) =6\\\\F(-1)=(-1)/(4) +(5)/(2) =(9)/(4) \\g(x)=(3x^2)/(2)+(x)/(2)-5\\\\G(x)=(x^3)/(2) +x^2-5x\\\\G(2)=4+1-10=-5\\\\G(-1)=(-1)/(2) +(1)/(4) +5=(19)/(4) \\\\\int\limits^2_(-1) {(f(x)-g(x))} \, dx =F(2)-G(2)-(F(-1)-G(-1))\\\\=11+(5)/(2) =(27)/(2)`