anonymous
  • anonymous
Find the volume of the solid formed by rotating the region enclosed by x=0 x=1 y=0 y=9+x3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
What is the axis of rotation? I'll assume we're letting y = 0 be the axis of rotation. The volume of a solid is given by: \[V = \int\limits_{a}^{b}A(x)dx\] where A(x) is the area of a cross section made perpendicular to the x-axis. Since we are rotating, the cross section is a circle. Its radius is given by f(x) = 9 + x^3 - 0 = 9 + x^3. \[A = \pi (9 + x^3)^2\] We are finding the volume from x = 0 to x = 1, so \[V = \pi \int\limits_{0}^{1}(9+x^3)^2dx\] Using the fundamental theorem of calculus, you should find that the volume is (1199/14)*pi

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