Answer to Question #342419 in Calculus for Jane

Question #342419

Find the area of f(x) = 3+2x-x² above the x-axis.

1
Expert's answer
2022-05-19T18:46:21-0400
3+2xx2=03+2x-x^2=0

(x+1)(x3)=0-(x+1)(x-3)=0

x1=1,x2=3x_1=-1, x_2=3A=13(3+2xx2)dxA=\displaystyle\int_{-1}^{3}(3+2x-x^2)dx

=[3x+x2x33]31=\bigg[3x+x^2-\dfrac{x^3}{3}\bigg]\begin{matrix} 3 \\ -1 \end{matrix}

=9+99(3+1+13)=323(units2)=9+9-9-(-3+1+\dfrac{1}{3})=\dfrac{32}{3}({units}^2)


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