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Student Solution Manual for Mathematical Methods for Physics and Engineering, Third Edition by M. P. Hobson, K. F. Riley

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6

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Multiple integrals

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6.1  Identify the curved wedge bounded by the surfaces y2 = 4ax, x + z = a and z = 0, and hence calculate its volume V.

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  As will readily be seen from a rough sketch, the wedge consists of that part of a parabolic cylinder, parallel to the z-axis, that is cut off by two planes, one parallel to the y-axis and the other the coordinate plane z = 0.

For the first stage of the multiple integration, the volume can be divided equally ...

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