5. Consider the 3D solid in the first octant bounded by the coodinate planes and the surface z-5-1²-y. (a) Sketch a graph of the shadow onto the zy-plane in the space provided. The graph need not be to scale, but number the axes so that important points can be read from the graph. Shade in the region. (b) Express the volume of the solid described above as a triple integral in the order of integration dz dy dx or dz dx dy.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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5. Consider the 3D solid in the first octant bounded by the coodinate planes and the surface
z-5-1²-y.
(a) Sketch a graph of the shadow onto the zy-plane in the space provided. The graph need not
be to scale, but number the axes so that important points can be read from the graph. Shade in
the region.
(b) Express the volume of the solid described above as a triple integral in the order of integration
dz dy dx or dz dx dy.
(c) Find the volume of the solid by evaluating your answer to part (b).
Transcribed Image Text:5. Consider the 3D solid in the first octant bounded by the coodinate planes and the surface z-5-1²-y. (a) Sketch a graph of the shadow onto the zy-plane in the space provided. The graph need not be to scale, but number the axes so that important points can be read from the graph. Shade in the region. (b) Express the volume of the solid described above as a triple integral in the order of integration dz dy dx or dz dx dy. (c) Find the volume of the solid by evaluating your answer to part (b).
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