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A: In cylindrical coordinate, x=rcosθ;y=rsinθ;z=zAnd,dV=rdrdθ
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A: We will use spherical coordinates
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A: We will find out the required expression for this given integral in cylindrical coordinate.
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A: Transformation from Cartesian (x, y, z) to Cylindrical coordinates:
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Q: Evaluate the cylindrical coordinate integrals
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Q: Convert the integral from rectangular coordinates to both cylindrical and spherical coordinates, and…
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Q: Convert the integral from rectangular coordinates to both cylindrical and spherical coordinates, and…
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- Evaluate ∭Rx2+y2−−−−−−√dV, where R is the region that lies inside the cylinder x^2+y^2=16 and between the planes z=−3 and z=2. (Hint: use cylindrical coordinates)Use spherical coordinates.Evaluate∭z dV, where E is between the spheres x ^ 2 + y ^ 2 + z ^ 2 = 16 andx ^ 2 + y ^ 2 + z ^ 2 = 25 in the first octant.Use cylindrical coordinates.Evaluate the triple intergral 5(x3 + xy2) dV, where E is the solid in the first octant that lies beneath the paraboloid z = 4 − x2 − y2.
- Find an equation of the form z = f (r, θ ) in cylindrical coordinates for z^2 = x^2 − y^2.Disregard the differential lengths and imagine that the object is part of a spherical shell. It may be described as 3 # r # 5, 60° # u # 90°, 45° # f # 60°where surface r 5 3 is the same as AEHD, surface u 5 60° is AEFB, and surface f 5 45°is ABCD.Find an equation of the form r = f (θ, z) in cylindrical coordinates for the following surfaces. z = x + y
- Given P(-11, 0, 49) in rectangular coordinate system, what is ρ (rho) in cylindrical coordinates? (Compute up to 4 decimal places)Find the volume of the solid bounded by the graphs of the given equations (given in cylindrical coordinates). r2 + z2 = a2 and r = a(cos(theta)) a=4Use spherical coordinates.Evaluate∭e ^ (x ^ 2 + y ^ 2 + z ^ 2) dV,where E is inside the sphere x ^ 2 + y ^ 2 + z ^ 2 = 25 in the first octant.