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+2x-x^2=0"

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

"x_1=-1, x_2=3""A=\\displaystyle\\int_{-1}^{3}(3+2x-x^2)dx"

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

"=9+9-9-(-3+1+\\dfrac{1}{3})=\\dfrac{32}{3}({units}^2)"


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