6.2 volumes on a base

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Volume from a to b:

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dxxAb

a V

Find the volume of solid S:

Ex 1: The base of S is an ellipse: 9x2 + 4y2 = 36. The cross-

sections perpendicular to the x-axis are isosceles right triangles with the hypotenuse in the base.

Find the volume of solid S:

Ex 2: The base of S is the triangular region with vertices (0, 0), (3, 0), and (0, 2). Cross-sections perpendicular to the y-axis are semicircles.

Find the volume of solid S:

Ex 3: The base of S is the triangular region with vertices (0, 0), (3, 0), and (0, 2). Cross-sections perpendicular to the x-axis are equilateral triangles.

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