Answer to Question #344322 in Calculus for Jane

Question #344322

1) Find the area bounded by the curve y-9-x and the x axis.



a) Horizontal Strip



b) Vertical Strip

1
Expert's answer
2022-05-24T23:01:26-0400

1)


"9-x^2=0=>x_1=-3, x_2=3"

a)


"y=9-x^2=>x=-\\sqrt{9-y}\\ or \\ x=\\sqrt{9-y}"

"A=\\displaystyle\\int_{0}^{9}(\\sqrt{9-y}-(-\\sqrt{9-y}))dy"

"=2\\displaystyle\\int_{0}^{9}\\sqrt{9-y}dy=2\\big[-\\dfrac{2}{3}(9-y)^{3\/2}\\big]\\begin{matrix}\n 9 \\\\\n 0\n\\end{matrix}"

"=-\\dfrac{4}{3}((9-9)^{3\/2}-(9-0)^{3\/2})=36({units}^2)"


b)


"A=\\displaystyle\\int_{-3}^{3}(9-x^2)dx=\\big[9x-\\dfrac{x^3}{3}\\big]\\begin{matrix}\n 3 \\\\\n -3\n\\end{matrix}"

"9(3)-\\dfrac{(3)^3}{3}-(9(-3)-\\dfrac{(-3)^3}{3})=36({units}^2)"



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