Answer to Question #342421 in Calculus for Jane

Question #342421

Determine the area of the region bounded by x = y²-y-6 and x = 2y +4.

1
Expert's answer
2022-05-22T23:45:20-0400
"y^2-y-6=2y+4"




"y^2-3y-10=0"

"(y+2)(y-5)=0"


"y_1=-2, y_2=5"




"A=\\displaystyle\\int_{-2}^{5}(2y+4-(y^2-y-6)dy"




"=[-\\dfrac{y^3}{3}+\\dfrac{3y^2}{2}+10y]\\begin{matrix}\n 5 \\\\\n -2\n\\end{matrix}"


"=-\\dfrac{125}{3}+\\dfrac{75}{2}+50-(\\dfrac{8}{3}+6-20)=\\dfrac{343}{6}({units}^2)"

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