Section 9.2 Area of a Surface of Revolution. THE AREA OF A FRUSTUM The area of the frustum of a cone is given by.

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Section 9.2 Area of a Surface of Revolution

THE AREA OF A FRUSTUM The area of the frustum of a cone is given by

FINDING THE SURFACE AREA OF A SOLID OF REVOLUTION Divide the interval [a, b] into n equal subintervals. Find the area of the conical frustums created by each subinterval. Sum the areas and take limit as the length of the subintervals go to zero. Compute definite integral.

Let f be positive and have a continuous derivative. The surface area of the surface obtained by rotating the curve y = f (x), a ≤ x ≤ b, about the x-axis is If the curve is x = g(y), c ≤ y ≤ d, then NOTE: For both cases, S = ∫ 2π y ds REVOLUTION ABOUT THE x-AXIS

REVOLUTION ABOUT THE y-AXIS For rotation about the y-axis, the surface area formula is S = ∫ 2π x ds where