To express: The limit (a) in terms of volume of solid (V) using the method of cylindrical shell.
The expression of the limit (a) in terms of V is .
The co-ordinates of the triangular region are , and .
The equations are , where .
Plot a graph using the co-ordinates of the triangular region are and :
Draw the shell as shown in Figure 1.
Calculate the volume using the method of cylindrical shell:
Substitute 0 for a, 1 for b, for x, and 2x for in Equation (1).
Integrate Equation (2).
Rearrange Equation (3).
Hence, the expression of the limit (a) in terms of V is .
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