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MC 2025 In-course Diagnostics for Undergraduate Mathematics MATH140 WP

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In evaluating the integral which integration technique would be most appropriate?

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Which would be a good choice for if the method of integration by parts was applied to evaluate

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Consider the region enclosed by the graph of and  The volume that is generated when is revolved about the -axis is represented by the integral:
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Consider the region enclosed by the graph of and the -axis. The volume that is generated when is rotated about the -axis is represented by the integral:
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Consider the region enclosed by the graph of and  The volume that is generated when is revolved about the -axis is represented by the integral:
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Consider the region  enclosed by the graph of and the line

.  The volume that is

generated when

 is revolved about

the line

is represented by the

integral:

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The volume of the solid generated when the region bounded by and  is revolved about the -axis is:
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Consider the region enclosed by the graph of and for The volume that is generated when is revolved about the -axis is represented by the integral:
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The volume of the solid generated when the region bounded by and is revolved about the y-axis is:
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The volume of the solid generated when the region bounded by and is revolved about the -axis is:
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