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Follow the steps to compute the volume of the solid obtained by rotating the region bounded by y=x^(2)quad" and "quad y=6x about the line x=0 using the method of disks or washers. a. Using the method of disks or washers, set up the integral. {:[V=int_(a)^(b)◻],[" with "a=◻" and "b=]:}

Follow the steps to compute the volume of the solid obtained by rotating the region bounded by\newliney=x2 and y=6x y=x^{2} \quad \text { and } \quad y=6 x \newlineabout the line x=0 x=0 using the method of disks or washers.\newlinea. Using the method of disks or washers, set up the integral.\newlineV=∫ab□ with a=□ and b= \begin{array}{l} V=\int_{a}^{b}\square \\ \text { with } a=\square \text { and } b= \end{array}

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Q. Follow the steps to compute the volume of the solid obtained by rotating the region bounded by\newliney=x2 and y=6x y=x^{2} \quad \text { and } \quad y=6 x \newlineabout the line x=0 x=0 using the method of disks or washers.\newlinea. Using the method of disks or washers, set up the integral.\newlineV=∫ab□ with a=□ and b= \begin{array}{l} V=\int_{a}^{b}\square \\ \text { with } a=\square \text { and } b= \end{array}
  1. Identify Intersection Points: Identify the bounds of integration by finding the intersection points of y=x2y = x^2 and y=6xy = 6x. Set y=x2y = x^2 equal to y=6xy = 6x: x2=6xx^2 = 6x x2−6x=0x^2 - 6x = 0 x(x−6)=0x(x - 6) = 0 x=0x = 0 or x=6x = 6
  2. Set Up Integral Using Washer Method: Set up the integral using the washer method. The outer radius R(x)R(x) is from the x-axis to y=6xy = 6x, and the inner radius r(x)r(x) is from the x-axis to y=x2y = x^2.
    R(x)=6xR(x) = 6x
    r(x)=x2r(x) = x^2
    Volume V=π∫x=0x=6[R(x)2−r(x)2] dxV = \pi \int_{x = 0}^{x = 6} [R(x)^2 - r(x)^2] \, dx
    V=π∫06[(6x)2−(x2)2] dxV = \pi \int_{0}^{6} [(6x)^2 - (x^2)^2] \, dx

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