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Published byFelicity Marker Modified over 3 years ago

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Tyler Ericson Stephen Hong

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When finding the volume of a solid revolving around the x-axis, use this formula… V = π

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Find the volume of a solid of revolution obtained by rotating the first quadrant regions bounded by the curve y = x 3, line x = 2 and the y-axis about the x- axis.

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V = π V = π(x 7 /7)| V = 128π/7 Determine the interval and plug into formula Simplify Integrate and solve

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V = π Plug the function being rotated into the formula Simplify

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V = π(2x 2 )| V = π [2(1 2 )- 2(0 2 )] V = 2π Integrate the simplified solution Solve using the given interval

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When you have two functions and you have to find the area of a region bounded by the two functions revolved around the x-axis use the formula: V = π

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Find the volume of a solid of revolution obtained by rotating the first quadrant regions bounded by the curve y = x 3 and line y = x around the x-axis.

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x = x 3 at x = 0, 1 x is the outer function and x 3 is the inner function Determine the interval by finding where the two functions intersect Then determine which is the inner and outer radiuses by looking at the graph

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V = π V = π(x 3 /3 – x 7 /7)| V = π[(1/3)-(1/7)] V = 4π/21 Plug in the values into the formula Simplify the integral Integrate Solve

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Always put dx at the end of your integrals Dont forget the π!!!!! Square before subtracting when using the washer method Solids of revolution have been a FRQ topic for the past 6 years

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Review: Volumes of Revolution. x y A 45 o wedge is cut from a cylinder of radius 3 as shown. Find the volume of the wedge. You could slice this wedge.

Review: Volumes of Revolution. x y A 45 o wedge is cut from a cylinder of radius 3 as shown. Find the volume of the wedge. You could slice this wedge.

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