Find area of the region between y = xe and its asymptote in the first quadrant. A) 1 В) 2 С) 3 D) 4 E) 5

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y? + z2 99 and the upper cone z? = 3x2 +…

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Q: "ind the volume of the solid obtained by rotating the region = 2y – y², x = 0,

A: x=2y-y2  x=0

Q: Find the value(s) of c such that the area of the region bounded by the parabolae y=x2-c2 and y=c2-x2…

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Q: Evaluate , ydV where E is the hemispherical solid region x? + y? + z? 0.

A: x^2+y^2+z^2 <=64, y>=0

Q: b) Find the volume of the region in the first octant bounded by the planes shown in the figure.…

A: Given: The equation of the plane is  y + z = 2 The equation of the cylinder is  x = 4 − y2 he volume…

Q: Find the volume generated by the equation x? + y² – 4x – 6y – 12 = 0 if it is rotated about the line…

A: The volume of the solid generated by resolution can be calculated by calculating the surface area of…

Q: and stra ight and x:8 Let R be an area enclosed by a curve. : 1 Using the disc method, which is the…

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Q: Let D be the region in the ry-plane inside the unit circle x? + y? = 1. Evaluate the double integral…

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Q: B) Show that V=367 is the volume of a sphere of radius 3 by using spherical coordinates.

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Q: Evaluate the double integral V1 + 4x² + 4y²dA, where D is the region inside the circle x + y? = 25…

A: We have to find area of the region bounded by the circle given in the first quadrant of the plane.

Q: Find the uolume Ihe solid obtoined by rotatting the region enclosed by y= obout The line y-l

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Q: Use Green's theorem to evaluate O(1-y') dx+(x³ +e" ) dy , where C is the boundary of the region…

A: The integral is ∮C1-y3dx+x3+ey2dy where C is the boundary of the region between the circles x2+y2=4…

Q: 5. Find the volume of liquid needed to fill a sphere of radius R to height h (Figure 18). R h…

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Q: V=$t re h for r (geometry, volume of a spherical tuumor).

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Q: Reduce the surface integral ( S A.ds) of a cube of sides parallel to the three perpendicular axes,…

A: Here we can use divergence theorem to reduce the given surface integral. Divergence theorem states…

Q: Calculate the area of the surface S. x2 that lies between z = 2 and z 6. S is the portion of the…

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

Q: 2. Fnd the area of the sur face in the first octant cut from the cone z2 = x2 y2 by the plane x +y =…

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Q: The area of the surface p = 2, 0sz<5,0<¢< T is 201 Select one: O True O False

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Q: 1. SSR ry? dA, where R is the region in quadrants 1 and 2 bounded by the semicircle of radius 2…

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Q: Consider the paraboloid z = 1- ² – y?. Find the volume of the region between this surface and the ry…

A: According to the problem,. we have

Q: Find the surface area of the part of the circular paraboloid z = x + y that lies inside the cylinder…

A: Solve the given

Q: 10. Determine the surface area of the part of z = xy that lies in the cylinder given by x² + y² = 1.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the value(s) of c such that the area of the region bounded by the parabolae y=x^2 - c^2 and…

A: Given: The given parabolas are y=x2-c2 and y=c2-x2. Determine the points of intersection.…

Q: Consider the solid whose base is the region bounded by 4x? + 9y? = 36. Y 3 -3 -2 -1 -1 2 3 2 -3 1.

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Q: (d) Consider the parallelepiped P in R³ whose adjacent sides are (0, 4, 0), (3, 0, 0) and (-1, 1,…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: (b) By using double integrals, find the surface area of the portion of hemisphere z = /25 – x2 – y²…

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Q: Use geometry to evaluate ∫∫∫R 1 dV where R is the region inside the sphere x2+y2+z2=4.

A: Given R as the region inside the sphere

Q: find the region endlased R by the cunes V=12-2y +1 and Y= -2+2x ャ4.

A: Answer

Q: Evaluate the integral R Vr + y² dA, where R is the region inside the upper semicircle of radius 2…

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Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x 450. c and y = c – x² is…

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Q: Integrate g(x, y, z) = x + y + z over the portion of the plan 2x + 2y + z = 2 that lies in the first…

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Q: The volume of the parallelepiped is Volume = |a x b||c|| sin | = |(a × %3D b). c| True False

A: Using direct formula

Q: Determine by direct integration the volume of the paraboloid shown in the figure below [units^3] if…

A: y = x2/b

Q: Find the area of the part of the sphere r? + y + z² = 4 that lies within the first octant and inside…

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Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 3 and the upper cone z? = 4x2 +…

A: Let's find.

Q: Find the volume of the ellipsoidal solid given by 4x² +4y² +z? = 16

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Q: Find c > 0 such that the area of the region enclosed by the parabolas y = a? – c² and y = c – a? is…

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Q: (b) Find the volume under the paraboloid z=x+y² above the triangle enclosed by the lines y=x, x=0…

A: To find the volume of the given solid.

Q: The volume of the parallelepiped is Volume = |a x b||c|| sin o| = |(a x b)- c| %3D %3D True False

A: We have to check either the volume of parallelepiped is volume=a×bcsinϕ=a×b·c or not.

Q: Evaluate ffp(4xy + 1) dA, where R is the region in the upper half-plane bounded by the circles a? +…

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Q: Calculate the area of the surface S. x2 y² _ z2 that lies between z = 2 and z = 6. S is the portion…

A: Explained below

Q: 8. Show that the volume of the region bonded by the cone z = Vx² + y² and the paraboloid z = x? + y²…

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Q: Find the area of the portion of the sphere x2 + y² + inder x2 + y? = 6y. %3D

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Q: Find the volume of the solid that lies under the elliptical paraboloid z = 2x2 + y? +4 and above the…

A: Given, z=2x2+y2+4 To find Volume of Solid

Q: B is the first quadrant part of the region enclosed by the circles x2 + y? = a? and x2 + y? = b2…

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Q: Find c > 0 such that the area of the region enclosed by the parabolas y = 390. c and y = c² – a? is…

A: we know that areaA of the region enclosed by given parabola is given by A=2∫-ccc2-x2dx=4∫0cc2-x2dx…

Q: O Find the volume of solid in the first octant bounded by the co- ordinate planes, the planes x-3,…

A: We will find out the required volume of the solid in the first octant.

Q: 1. Find So(r+2y)dA, where D is the region bounded by the parabolas y r, and y=1+

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Q: Use the theorem of Pappus to find the volume of a torus (pictured here). Assume that a disk of…

A: We know by the theorem of Pappu that the volume of a solid is obtained by area times the distance…