volume of the solid generated

Q: Find the volume of the solid obtained by rotating region A about the given axis, x = 2.

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Q: Let B be the solid whose base is the circle x^2+y^2=49 and whose vertical cross sections…

A: Given, Circle- x²+y²=49=7² --------equation 1 The equation is of the form x²+y²=r². Therefore, the…

Q: Find the volume of the solid generated when R is revolved about the given

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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 of the torus generated by revolving the region bounded by the graph of the circle…

A: given x-112+y2=1 claim- to find the volume of torus generated by revolving the region bounded by the…

Q: Find the volume generated by rotating the given region about the specified line. R, about AB

A: On revolving the region R1 around the line Ab, the resulting solid obtained will be a cone.   This…

Q: Let B be the solid whose base is the circle (x^2) + (y^2) = (4^2)  and whose vertical cross sections…

A: This question is based on application of Integration.

Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

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Q: A volume is described as follows: 1. the base is the region bounded by æ = – y² + 2y + 98 and æ 2.…

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Q: Find the volume of the torus generated by revolving the region bounded by the graph of the circle…

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Q: If the region R = {(x, y) | x > 1,0 < y < 1/x} is rotated about the x-axis, the volume of the…

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Q: The base of a solid is the region between the curve, y?(p + x) = x²(3p – x), 0 < x < 3p,y 2 0 and…

A: The solution is given below

Q: b) y = 1<x< 4 about the y-axis

A: To find the volume of the solid obtained by rotating the given region about the specified line y=1x…

Q: (a) Sketch the region bounded by the graphs of y = x + 1, y = x2 – 1, x = 1, and x = 2. (b) Use the…

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Q: Discover the volume of the solid region in the first octant bounded by the coordinate planes and the…

A: Equation of given surface = z= 5-x^2-y  dV = dx dy dz

Q: ind the volume of the solid whose base is a circular disk of radius R, centered at the origin and…

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Q: Find the volume of the region in the first octant cut from the solid sphere ps 6 by the half-planes…

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Q: Find the "volume" of the four-dimensional pyramid bounded by w +x+ y+z-1=0 and the coordinate planes…

A: The volume of the four dimensional pyramid is given by, V=∫v1 dv   =∫dzdydxdw. The boundaries are…

Q: find the volume of the solid generated when R is revolved about the x-axis

A: Given that R is the region enclosed by the curve y=cosx, y=ex, x=π2 The volume of the solid…

Q: 5. Use the method of Washers and Shells to find the volume of the solid generated when the region R…

A: Given, y=x2over [0,2] is revolved about the line y=-2.

Q: The base of a solid is the region between the curve, y?(p + x) = x²(3p – x),0 0 and the X – axis.…

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Q: (a) Show that the volume of the solid in R³ that lies below the surface z = f(x, y) and above the…

A: We will set the tripple integral for the volume then deduce a double integral on domain D  Then we…

Q: The base of the solid S is the region enclosed by the graph of y=sqrtln(x), the line x=e and the…

A: Given The base of the solid S is the region enclosed by the graph of y=sqrtln(x), the line x=e and…

Q: b) Find the volume of the solid which is in the first octant and bounded between the spheres p = 1…

A: To find- Find the volume of the solid which is in the first octant and bounded between the spheres ρ…

Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

A: According to the given information, it is required to calculate the volume of the solid generated by…

Q: B. Find the volume of the solid generated when the plane region bounded by 4. y =, x = 1, x = 4, and…

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Q: Find the volume cm^3 of the solid figure in Fig 1182 that was generated by rotating the shaded…

A: Volume of revolution

Q: If the region R = {(x, y) | x 2 1, 0 sys 1/x} is rotated about the x-axis, the volume of the…

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Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

A: Given data:     The given function is: y=2(x)1/4. The given limits of y is: [a,b]=[0,2].   The given…

Q: (a) sketch the region enclosed by the curves, (b) describe the cross section perpendicularto the…

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Q: Find the volume generated by rotating the given region about the specified line. R, about BC

A: In this question, we find the volume by rotating the region R1 about the line BC.

Q: tegral in Geometry, Science, and Engineering 23. x= y', x = y+ 2

A: Given: x=y2, x=y+2

Q: Let a sphere of radius r be cut by a plane, thereby forming a segment of height h. Show that the…

A: Sphere was cut at height h, radius of the circle at intersection of 2 cuts is r2-h2. Similarly…

Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

A: The given figure is,

Q: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=2 is a. 2 Ob. 32

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Q: (a) Sketch the region bounded by the graphs of y = x + 1, y = x2 – 1, x = 1, and x = 2. %3| %3D |…

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Q: 5. Find the volume under the paraboloid = -a? – y?, and above the cone z = - p² + y?.

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Q: Find the volume V of the solid below the paraboloid z = 6-x -y and above the following region.

A: We have to calculate ∬Rz dxdy

Q: 1. Find the volume of the solid obtained by rotating the region bounded by the curve y? = x?(a – x),…

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Q: Find the volume of the solid the region Cut of from the sobd Reft Ža? by the hae half-plane - and…

A: The spherical coordinates are given by  x=ρsinφcosθy=ρsinφsinθz=ρcosφ Hence the equation x2+y2+z2…

Q: If the region bounder by the two curves is revolved about x = 4, what is the volume of the resulting…

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Q: Let R be the region enclosed by the graphs of y =e¯*,y=e", and x = 1. What is the volume of the…

A: Given- Let R be the region enclosed by the graphs of y = e-x, y = ex, and x = 1.  To find- What is…

Q: A solid is contruc lines x = a, x = b, the graph of y = f(x) and the x-axis, and the cross-sections…

A: To find the volume of the solid.

Q: The base of a solid is the region in the first quadrant bounded by the coordinate axes, and the line…

A: Volume of the solid

Q: (c) Find the volume of the solid generated by revolving the region enclosed by the triangle with…

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Q: A disk bounded by the circle z +y = a² is revolved about the y-axis to make a sphere. A hole of…

A: Consider the provided question, A disk bounded by the circle x2+y2=a2 is revolved about the y-axis…

Q: A volume is described as follows: 1. the base is the region bounded by æ = - y? + 10y + 95 and æ =…

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Q: Show that the volume of the region bonded by the cone z=/x +y and the paraboloid z x+y is a/6.

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Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

A: The region is bounded by the curve y=6x1/4 and y=6. The region rotated by the line AB is x=1.…

Q: Let a sphere of radius r be cut by a plane, thereby forming a segment of height h. Show that 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.