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Q: ³ y = 2.x, y = 3x – x )A region is bounded by O Rotate around the x-axis b) Rotate around y = 4 Use…

A: Part a) The volume generated by y = 2x and y=3x-x3 and rotated around x-axis is shown below:…

Q: 2. Given a tetrahedron with vertices (0,0,0), (3, 0, 0), (0,6 0), and (0, 0, 4). Express the volume…

A:

Q: . An area bounded by y = 0, x = 0, and y = e-x, is revolved about the x-axis. CD method is…

A:

Q: Seqion bounded by X=y2 4:3 2S kelch Fue cind b Set up tLe Integrels to geti the volume of the solid…

A: The given region is bounded by x=y2, x=0 and y=3.

Q: Hw.4 heights ave defined by ECX,y) and bases are the regions bounded by the fottowing fon ttiow in…

A: Volume bounded by xy-plane

Q: The design of a new airplane requires a gasoline tank of constant cross-sectional area in each wing.…

A:

Q: 80 y 60- 1.0 0.5 40 0.5 1.0 1.5 -0.5 -1.0 -5 y y 1.0 50 0.5 8 -1.0 -0.5 0.5 1.0 1.5 -50 -0.5 -1.0F…

A: The last graph is the correct graph.

Q: Let Sbe the solid in the first octant situated between the planes z+y+z=6and 3z +3y+ 2z - 18. Find…

A:

Q: 15. The region within X= 9-y and between the lines X-y-7= 0 and x = 0 is revolved about the line y =…

A: In the question we have to find volume using shell method.

Q: . The region within X=9-y and between the lines X-y-7= 0 and x = 0 is revolved about the line %3D y…

A: The region given is x=9-y2 and it is bounded by the lines x-y-7=0 and x=0 which is revolved about…

Q: A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2…

A:

Q: 7 The volume of the solid region 7 = Is (A) 120T (B) 100T (C) 132T (D) 967 {(x, y, z) € R³: 4≤2² +…

A:

Q: Firnd the volume ul lhe lhe solid formed by revolving the regiun bounded by y-5-x; y-0; aboul…

A: The volume of the solid of the revolution can be calculated by the formula . Here, a is the lower…

Q: 15. Yogurt containers can be shaped like frustums. Rotate the line y = x around the y- axis to find…

A: 15.   yougurt containers can be shaped like frustrums.Rotate the line y=1mx around the y-axis…

Q: Solids of revolution Determine the volume generated about y-axis the area enclosed by: y²- 4y + 2x =…

A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

Q: Find the center of mass of an object that occupies the upper hemisphere of x2 + y² + z? = 1 and has…

A: The center of mass can be calculated using the formula x=Myzm, y=Mxzm, z=Mxym. Here, Mij are the…

Q: Home work.2 für fiyure shan below. find volume of the slarded a IF you Knos Pmt the dimensinn…

A: In first problem,height of the solid 2km= 2000m, since given value on x-axis is 2m. Volume= (base…

Q: 1. A rectangular box is placed in the first octant, with one corner at the origin and the three…

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Q: H.W : The region bounded by the curve y= x² and the line y=3x is revolved about a) x-axis b) y-axis…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: : Deter min e the volumew of revolution obtained by rotating the region bounded by y = V9- x², 3y+ x…

A:

Q: Determine whether the following statements are true and give an explanation or counterexample. a. A…

A: (a) The shell method is a method of finding volumes by decomposing a solid of revolution into…

Q: 22 Let T be the triangle in the xy plane enclosed by the line y = 4x and the x-axis between x = 0…

A: Given that  The line is y=22x/7 To find the volume of the c  Where C is the cone obtained by…

Q: W is the volume defined by x2 + y² + z? < 1 and y < x. Find the flux of F= (x³ - 3x)i+ (y³ + xy)j+(…

A:

Q: 2 S- /x² +y? and z= /x? +y? volume V = | T Enter an integer or a fully reduced fraction such as 1 ,…

A: Volume , V = ∫∫∫dV = ∫∫∫R dz dy dx

Q: How.y The Solid shown in figure consists of a cone of radius r) and height (hit and a cylinder of…

A: Answer is in below steps.

Q: A solid is in the first octant lies inside the hemisphere √√x² + y², 2 = 4 – x² - y², outside the…

A:

Q: Let E be the region bounded cone z 3 - (z² + y³) and the sphere z = 102 2² – y . Provide an answer…

A: Given the region bounded by z=-3x2+y2 and the sphere z=102-x2-y2

Q: Hw.4 heights ave defined by ECX,y) and bases are the regions bounded by the fottowing funttion in…

A: Given: The heights of the solid are defined by zx,y=x2-xy, R:   y=x   and     y=3x-x2 To find:…

Q: 2Det up a double ander the graph of fcexiyo=y reaion with vertices (2,2), (4,4) and (G, 2), integral…

A: Let R be the triangular region with vertices (2,2), (4,4) and (6,2). Set up a double integral to…

Q: 54. The area bounded by the curve x³ = y, the line y = 8 and the y-axis is to be revolved about the…

A: Given question:- The are abounded by the curve x3=y, the line y=8 and the y-axis is to be revolved…

Q: used Thank you for answering this question. Please you specify each step and formula as soon as…

A: Solve by triple integration

Q: 13. A right circular cylinder is inscribed inside a sphere with radius r 3 inches. Find the maximum…

A:

Q: et up, but do not evaluate, the volume of the solids generated by rotating the regions bounded v y =…

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Q: find the center of mass X = 2sint y = 2 cos t • Z = 3€ ( the densily is a constant k )

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Q: Find the mass M and center of mass x of the linear wire covering the given interval and having the…

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Q: 15. The region within X= 9- y' and between the lines X-y-7=0 and x = 0 is revolved about the line y…

A:

Q: OL B 22. Find the volume of the solid formed by the region formed by: x = 2,/y, y = x, rotated…

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Q: A region R is bounded by the graphs of y=0.1 Vx and y=0.1x. Find the moments My and My of R about…

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Q: 5. Use differentials to app. .. the value of V(3.01)² + 2(0.99) – 3 in four decimal places. o 5.…

A: I am attaching image so that you understand each and every step. Let x= length of box y=width of box…

Q: 9) use the snell metnod to sef up end eveluete tueinteyrel tret gives the volume of the solid…

A: Using shell method, volume is evaluated.

Q: Experiment the following Questions using MATLAB 1. The region bounded by the curve y =x' +1 and the…

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Q: Q5\ For what value of the constant 'a' does the volume of the region under the surface z = ax+3y…

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Q: Find the volume of a solid generated by revolving, about the y-axis, the region bounded by y = 2e* ,…

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Q: 39 Find the volume inside the sphere (r = a) that lies between the cones ( = 1/3) and ( = 2n/3) %3D

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Q: Find the volumes of the solids obtained by rotating the region bounded by the curves y=√√x and y=x²…

A:

Q: a. Find the center of mass of a thin plate of constant density cov-ering the region between the…

A: (a)Given information:

Q: e circular disk method is to be used to compute for the volume of the solid gene revolving the…

A: Top:- application of integration

Q: XIX. Find the volume bounded by z = 9– x² – y and z = 0. Give a numerical %3D answer.

A:

Q: 2) Find volume from above Z = 14-a-yz below Z=o inside 2+y%=|

A: The given problem is to find the volume of the solid bounded by given region and inside the region…

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.