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Cartesian Form:
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Area of solid formed by revolving the arc of curve about x-axis is-
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Area of revolution by revolving the curve about y axis is-
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Area of solid formed by revolving the arc of curve about x-axis is-
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Parametric Form:
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About x-axis:
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About y-axis:
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About x-axis:
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Polar Form: r=f(θ)
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About the x-axis: initial line
Here replace r by f(θ) -
About the y-axis:
Here replace r by f(θ)
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About the x-axis: initial line
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About any axis or line L:
where PM is the perpendicular distance of a point P of the curve to the given axis. -
Limits for x: x = a to x = b
Here PM is in terms of x. -
Limits for y: y = c to y = d
Here PM is in terms of y.
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Limits for x: x = a to x = b
Example: Find the area of the solid of revolution generated by revolving the parabola
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