62. Let D be the region in the first octant that is bounded below by the cone o = 7/4 and above by the sphere p = 3. Express the volume of D as an iterated triple integral in (a) cylindrical and (b) spherical coordinates. Then (c) find V.

Q: 21) Use triple integral to find the volume of the part of sphere at the following region 0SRS Scm,…

A: Given that: 0≤R≤5π3≤∅≤π20≤θ≤π The Volume of sphere = 43πr3 Using the triple integral method solving…

Q: Let R be the region bounded by y = 9 – x and y = 2x+ 6 find the volume %D generated when R revolved…

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Q: 2) Find the volume of the solid bounded by the cylinder x2 + y = 16 and from z = 1 to z + x %3D 2…

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Q: iii. Find the volume of the solid bounded by z = 4 – x² – y in the first octant.

A: To find the volume of the solid

Q: 27. Find the volume generated by rotating the area bounded by y = x² + x, x = 1, x = 4, and the…

A: Given that: y=x2+x,   x=1,  x=4   and   the   x-axis To sketch the graph,

Q: 45. Find the volume of the solid in the first octant bounded by the cylinders x² + y² = a², x² + z²…

A: First we will calculate the volume common to both the cylinders.  Parallel area perpendicular to x-…

Q: 8. Use a triple integral to find the volume of the solid shown z=1-y y=Vx-

A:

Q: 1. Find the volume of the solid obtained by rotating the area in the first quadrant bounded by y =…

A: As per our guidelines we are supposed to answer only one question. kindly repost others question as…

Q: by rotating Find the Volume oF the solid obtained bounde d by und X=4 y=o rotating y= 8 on

A:

Q: 7) Suppose that y, =sinx and y, = cos x on [0,4] %3D Find the volume if the region between y, and y,…

A: First we sketch the region using a graphing calculator The shaded region is rotating about the x…

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: 5. Which of the following integrals would correctly compute the volume of the shape obtained by…

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Q: he region bounded by y = e, y = 0, x = 0, and x = 1 is revolved about the y- xis. Find the volume of…

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Q: 1. Use a triple integral to find the volume of the solid the tetrahedron enclosed by 2x + y+ z 4 and…

A: Given data: The tetrahedron is enclosed by plane 2x+y+z=4 and coordinate planes.

Q: 3. Consider the region bounded by the y-axis, y = V3x + 1, and r = 4. Set up an integral to compute…

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Q: please set up the integral and find the volume. thankyou

A: The equation of cone with x axis as the axis of cone, is x2=y2+z2, |x|≤1 It is bounded by the planes…

Q: 6. Evaluate ffſ z² dx dy dz taken over the volume bounded by the surfaces x2 + y² = a?, x² + y² = z…

A: Solution is given below:

Q: 2. Find the volume of the region bounded by y = x3 and y = x rotated about %3D the x-axis.

A: In this problem we can use washer method to find the volume of the solid of revolution. Washer…

Q: 2) Find the volume generated by the area bounded by y = x², y = 4x, revolved about x-axis.

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Q: 2) ( ) Sketch and find the exact volume of the solid obtained by rotating the region B bounded by…

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Q: 4. Use double integral to find the volume of the solid enclosed by the following curves y = x and by…

A: Given that the solid is enclosed by curves y=x2 and by planes y+z=4 and z=0. It is required to find…

Q: 4) Find the volume of a solid generated by revolving about the x- axis the region bounded by y = x2…

A: We find the volume of a solid generated by revolving about the x- axis the region bounded by y = x2…

Q: 2. Give and evaluate a triple integral describing the volume in the first octant below the cone z =…

A: Given: Given the region in the first octant below the cone z=x2+y2 and above the paraboloid z=x2+y2…

Q: 1. Find the volume of the solid generated when the region bounded by y = 9 – x² and y = 2x + 6 is…

A:

Q: 10. Use a triple integral to find the volume of the solid region in the first octant between: z = x?…

A: The given problem is to find the volume of the solid region in the first octant between the two…

Q: 6. Evaluate ffS z² dx dy dz taken over the volume bounded by the surfaces x2 + y? = a?, x² + y² = z…

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Q: 5. Find the volume under the paraboloid z = -x² – y², and above the cone z = -. -V#²+ y².

A: Given

Q: e the Disk/Washer method to set up the integral that computes the volume of the solid created…

A:

Q: Let S be the solid in the first octant bounded by the cylinders x² +y² = 4 and x² + z² : -) Use…

A: The volume of the given solid S is V=∫∫∫S dVwhere solid is bounded by cylinders x2+y2=4 and…

Q: 8. Set up and evaluate the integral to find the volume of the smaller region cut from the solid…

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Q: (4) Find the volume of the solid obtained by rotating the region bounded by y y=√x about the y = 1.…

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Q: 5. Compute the volume of the region outside of the cylinder r² +y² = 16 and inside the sphere x2 +…

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Q: 12. Consider the region R bounded by the line y = 37 – 7x and the parabola y = 27 – x² . %3D Find…

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Q: 5. Find the volume of generated by rotating the region bounded by x = 4y – y? and x = 0 (a) about…

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Q: 2. Set up the integral(s) for finding the volume of the solid of revolution obtained by rotating…

A: We will find out the required volume of solid of revolution.

Q: 1. Find the volume of the solid obtained by rotating the area in the first quadrant bounded by y = T…

A: Given that y=x2, x=0, y=2-xaround the line x=1find the volume

Q: 3. Find the volume generated when the region defined by y = x, y = 2x/(1+ x³) is revolved around the…

A: NOTE : As per Bartleby rules incase of multiple questions only one is answered. Please upload others…

Q: Evaluate the integral of the volume of the solid formed by revolving the region bounded by x² + y =…

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Q: 5. If the first cylinder is x + y = a², where a 1?

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Q: 23. Find the volume of the solid formed by the region in the first quadrant bounded by: x = y - y, x…

A: *to find:- Volume of revolution of solid.

Q: 2) Find the volume of the solid that is bounded above by the cylinder z = x? and below by the region…

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Q: 12.Find the volume of the solid that is bounded above by the cylinder (z=x) and below by the region…

A: Given equation of cylinder, z=x2 and the equation of parabola, y=2-x2 and the line y=x To find the…

Q: 4. Use a triple integral to find the volume (set up and evaluate). z = V1 - x² – y² r = sin 0

A: As r=sinθ, then x=rcosθ=r1-sin2θ=r1-r2y=rsinθ=r2 The limits of integration are…

Q: 3. Find the volume of the resulting solid of revolution located in the first quadrant bounded by the…

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Q: 6. Find the volume of the solid obtained when the region bounded by y ==, y = 0,x = 1, and x = 2 is…

A: As per the our guideline, we are supposed to solve only first question. Kindly repost other question…

Q: 4. Find the volume of the solid obtained by rotating the region bounded by y = e", y = 0, x = -1, x…

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Q: 6) Use the washer method to find the volume of the solid generated by revolving the region y = x² +1…

A: We first sketch the region using a graphing calculator. From the graph, we see that x is from 0 to…

Q: 5. Find the volume generated by revolving the area under curve y = e from z = 0 to z = 1 (a) about…

A: Since solve the first question for you. If youwant any specific question to be solved then please…