Let E be the solid inside the cylinder x2 + y2 = 9, above the plane z = 1 and below the paraboloid z = x² + y². a) Sketch the solid and its projections b) Use rectangular coordinates to set up a double integral that expresses the volume of this solid. c) Convert all equations to cylindrical coordinates and simplify, d) Use cylindrical coordinates to set up a triple integral that expresses the volume of this solid. Recall x =r cos t, y =r sin t, z = z, dV = rdrdtdz.
Let E be the solid inside the cylinder x2 + y2 = 9, above the plane z = 1 and below the paraboloid z = x² + y². a) Sketch the solid and its projections b) Use rectangular coordinates to set up a double integral that expresses the volume of this solid. c) Convert all equations to cylindrical coordinates and simplify, d) Use cylindrical coordinates to set up a triple integral that expresses the volume of this solid. Recall x =r cos t, y =r sin t, z = z, dV = rdrdtdz.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Number 4 please
Transcribed Image Text:all equations to polar coordinates using the substitution x = r cos t, y = r sin t. Recall
that dA
= rdrdt.
4. Let E be the solid inside the cylinder x2 + y² = 9, above the plane z = 1 and below the
paraboloid z =
x2 + y?.
a) Sketch the solid and its projections
b) Use rectangular coordinates to set up a double integral that expresses the volume of
this solid.
c) Convert all equations to cylindrical coordinates and simplify,
d) Use cylindrical coordinates to set up a triple integral that expresses the volume of
this solid. Recall x =r cos t, y =r sin t, z = z, dV = rdrdtdz.
5. Consider solid E bounded by the elliptic cone 2y2 + x2 = z2 and below the plane z =
y+1.
a) Sketch the solid and its projections
b) Use rectangular coordinates to set up a triple integral that expresses the volume of
solid E.
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