Answer to Question #344323 in Calculus for Jane

Question #344323

2) Find the area bounded by the curve x = y² + 2y and the line x = 3.

1
Expert's answer
2022-05-26T07:54:01-0400
"y^2+2y=3"

"y^2+2y+1=4"

"(y+1)^2=4"

"y_1=-3, y_2=1"

"A=\\displaystyle\\int_{-3}^{1}(3-(y^2+2y))dy"





"=\\big[3y-\\dfrac{y^3}{3}-y^2\\big]\\begin{matrix}\n 1 \\\\\n -3\n\\end{matrix}"





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

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