The integral represents the volume of a solid of revolution. 2 pi integral^3_0 x

Question

The integral represents the volume of a solid of revolution. 2 pi integral^3_0 x^4 dx (a) Identify the plane region that is revolved. plane region bounded by y = x^4, y = 27, y = 0, x = 0 plane region bounded by y = x^4, y = 0, x = 0, x = 3 plane region bounded by x = y^3, x = 0, y = 0, y = 3 plane region bounded by y = x^3, y = 0, x = 0, x = 3 plane region bounded by y = x^3, y = 27, y = 0, x = 0 plane region bounded by y = x^1/2, y = 0, x = 0, x = 3 (b) Identify the axis of revolution. revolved about the x-axis revolved about the y-axis revolved around the line y = 3 revolved around the line y = 27 revolved around the line x = 27 revolved around the line x = 3

Explanation / Answer

(a) option 4th, Y = X3 , Y = 0, X =0 and X=3

(b) Option 2nd, Y axis

note: this is shell method notation for volume of rotation

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