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MAT136H1 Lecture : 6.2 Volumes Question #3 (Medium)

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UTSG
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Mathematics
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MAT136H1
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Question #3 (medium): interpreting the volume of a solid. , it is not hard to separate the components that make up the , the height of and the interval [ ]. If the integral is in terms of and , the area is rotated about a horizontal line. If the integral is written in terms , and , then the rotation is about a vertical line. Volume of a solid is expressed by the integral. Volume of a solid using integral is expressed as: where. So the expression inside the given integral follows that: Thus, represents a length, it is always positive. Then the solid is obtained by the region bound by and rotated about the -axis. The values fall within the interval given by the integral over [ ]. The values lie between and , where the top function is , and the bottom function is . { } of the -plane about the -axis.

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