A solid dome is to be constructed with the ellipse x2 + 3y² = 6 as a base. Using infinitely many semi-circles, determine the volume that this solid wi1l generate

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Q: Determine the volume if the area common with y²-3x+7y=8 and x²-4x+3=y² is revolved about the…

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Q: Find the exact volume of the solid of revolution that results when a semicircular region with…

A: We know that if as semicircle is rotated about diameter then resulted figure will be sphere, whose…

Q: A solid dome is to be constructed with the ellipse x^2+3y^2=6 as a base. Using infinitely many…

A: Given that the solid dome is to be constructed with the ellipse x2+3y2=6 as a base. We have to…

Q: 2 Find the volume of the region between the ellipsoid (=) = 1 and the plane 4 8. - | א + నా | co

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Q: Find the volume of the solid obtained by rotating the triangle with the vertices A(0,0), B(4,4) and…

A: Solution

Q: The base of a solid is the region bounded by the ellipse 4x2 + 9y? = 36. Find the volume of the…

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Q: Find the volume of the ellipsoid =D1 in positive octant Once

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Q: Find the volume of the solid whose base is the semicircle y = √9 - x² where -3 ≤ x ≤ 3, and the…

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Q: Find the volume of the region bounded above by the elliptical paraboloid z = 8 -3x-5y and below by…

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Q: Find the volume of the paraboloid, z = 9 - x² - y², that lies inside the cylinder x² + y² = 4.

A: It is seen that the paraboloid and cylinder both are extended upto negetive infinity of along z…

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Q: Find the volume of the solid generated by revolving the region enclosed by the ellipse 9x2 + 4y2 =…

A: Find the volume of the solid generated by revolving the region enclosed by the ellipse 9x2 + 4y2 =…

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Q: If the path defined by z(x) from points C to W were rotated about the x-axis, what would be the…

A: Given zx=-0.00001x6+0.00026x-0.00313x4+0.01704x3-0.01298x2-0.30265x+3.56157 To find the volume of…

Q: Find the volume enclosed by the cy linder (x-1) ty²=1 and the sphere x² +y²7z²=L4.

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Q: Use the Theorem of Pappus to find the volume of thegiven solid. The solid obtained by rotating the…

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Q: Determine the volume of the solid lying under the elliptic paraboloid z = 6y² – 2x² + 3 and above…

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Q: Use the theorem of Pappus a = 2 is positioned with the Volume = %3D Write as an exact expressi

A: .assume that a disk of radius a=2 is positioned within the left hand of the circle  at x=b=9 and is…

Q: 2. (2 - x² – y²)dydx

A: Given, I=∫01∫012-x2-y2dydx…

Q: Find the volume of c such that the area of the region bounded by the parabolas y = 16x2 - c2 and y =…

A: Given parabolas are y1=16x2-c2y2=c2-16x2 The area between the given parabolas is 1283

Q: A solid dome is to be constructed with the ellipse x^2+3y^2=6 as a base. Using infinitely many…

A: Graph the ellipse.

Q: Find the volume in the first octant bounded above by the paraboloid z = 9 – x² – y? and on the sides…

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Q: Find the volume of the region cut from the solid sphere ρ≤ a by the half-planes θ = 0 and θ = π/6 in…

A: Find the volume of the region cut from the solid sphere.

Q: Find the volume (in m3)  of a right truncated triangular prism with a triangular base whose sides…

A: Please follow step 2nd .

Q: Find the volume of the tetrahedron in the first octant that is bounded by the three coordinate…

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Q: What is the volume of the solid whose base is the interior of the parabola y2 = x from x=0 to x=4…

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Q: Find the volume of the solid bounded by the ellipic 4 + 5x² + 3y², the planes x paraboloid z = = 2…

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Q: rated by revolving the area bounded by the parabola y² = 8x and its latus rectum about the latus…

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Q: Suppose that a ring created by drilling a hole with radiusr through the center of a sphere of radius…

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Q: Find the volume of the solid generated by revolving the pentagon with vertices (1, 0), (2, 2), (0,…

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Q: Find the volume bounded by the paraboloid z = 1+ 3x? + 3y? and the plane z = 16 in the first octant.

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Q: = 1, 三 a NIU + +

A: Here Let u = x/a, v = y/b , w = z/c Then dx = a du, dy = b dv, dz = c dw So, Required volume V =…

Q: Find the volume generated by revolving the area bounded by the parabola x2 = 4y and its latus rectum…

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Q: Find the volume of the solid of revolution bounded by the circle +y = 16, and the lines 0 and

A: To find: Volume of the solid

Q: Find the volume of the wedge cut from the first octant by the cylinder x2 + y2 = 1 and the plane 2x…

A: To find the limits of x, y and z from the region of integration, substitute 0 for y.…

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Q: The base of a solid is bounded by the graph of x² + y² = a², where a > 0. Find the volume of the…

A: The base of the solid is the disk x2+y2≤a2, where a is the radius as shown below: The boundary…

Q: Find the dimensions of the closed right circular cylindrical can of smallest surface area whose…

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Q: 3. Suppose that a ring created by drilling a hole with radius r through the center of a sphere of…

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Q: Use the Theorem of Pappus to find the exact volume of a general cone created by rotating a triangle…

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Q: Determine the volume of the solid lying under the elliptic paraboloid z = 6y? – 2x2 + 3 and above…

A: To evaluate the integral

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the giveN…

A: Given: y=6-2x-x2 and y=x+6 about the x-axis. To find the volume of the solid bounded by the given…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: A right traingle of a given hypotenuse is rotated about one of its legs to generate a right circular…

A: Using Pythagoras theorem and by application of derivative we can find the maximum volume.

Q: Find the volume of the solid whose base is the semicircle y = v9 – x2 where -3 < x < 3, and the…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.