2. Let S be the solid cone bounded by z = Va? + y? and z = 3. (a) Sketch a picture of the solid S. (b) Our goal is to set up an iterated integral of the form ry=? 8(x, y, z) dz dy dx x=? y=? to represent the mass of S where d(x, y, z) tells us the density of S at the point (x, y, z). Our par- ticular task is to find the limits on each of the three integrals. Sketch the projection of the solid S onto the ry-plane. What are the least and greatest possible values of r overall? Fill in these limits first. Now, imagine that r is fixed. Referring to the projection of the solid onto the ry-plane, what are the least and greatest possible values of y? Your bounds for y will depend on r. Now, given a point (r, y), identify the least and greatest possible values of z. Your bounds for z may depend on r, y, or both.

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2. Let S be the solid cone bounded by z = Va? + y? and z = 3.
(a) Sketch a picture of the solid S.
(b) Our goal is to set up an iterated integral of the form
ry=?
8(x, y, z) dz dy dx
x=?
y=?
to represent the mass of S where 8(r, y, z) tells us the density of S at the point (r, y, z). Our par-
ticular task is to find the limits on each of the three integrals.
Sketch the projection of the solid S onto the ry-plane. What are the least and greatest possible
values of r overall? Fill in these limits first.
Now, imagine that r is fixed. Referring to the projection of the solid onto the ry-plane, what are
the least and greatest possible values of y? Your bounds for y will depend on r.
Now, given a point (r, y), identify the least and greatest possible values of z. Your bounds for z may
depend on r, y, or both.
Transcribed Image Text:2. Let S be the solid cone bounded by z = Va? + y? and z = 3. (a) Sketch a picture of the solid S. (b) Our goal is to set up an iterated integral of the form ry=? 8(x, y, z) dz dy dx x=? y=? to represent the mass of S where 8(r, y, z) tells us the density of S at the point (r, y, z). Our par- ticular task is to find the limits on each of the three integrals. Sketch the projection of the solid S onto the ry-plane. What are the least and greatest possible values of r overall? Fill in these limits first. Now, imagine that r is fixed. Referring to the projection of the solid onto the ry-plane, what are the least and greatest possible values of y? Your bounds for y will depend on r. Now, given a point (r, y), identify the least and greatest possible values of z. Your bounds for z may depend on r, y, or both.
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