How do you find the volume of the solid obtained by rotating the region bounded by the curves [Math Processing Error] and [Math Processing Error] about the x axis?

1 Answer
Aug 20, 2015

[Math Processing Error]

Explanation:

The region bounded by the two functions, a vertical parabola and a straight line is shown in the picture. On solving the two equations the points of intersection can be easily found to be[Math Processing Error] and (2,12)

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If [Math Processing Error] and [Math Processing Error]= 5x+2, consider an element of length [Math Processing Error] and width dx, of the region bounded by the two functions. If this element is rotated about x axis, the volume of the elementary disc so formed would be [Math Processing Error] dx.

The volume of the solid formed by rotation of the whole region, about x axis would be

[Math Processing Error]

[Math Processing Error]

[Math Processing Error]

On solving, this integral would work out to be=[Math Processing Error]