Find the center of mass of the region between the curve y = 1/I and the x-axis from I =1 and x = 2.

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: Ans:-  we have to fid the volume of the solid                obtained by rotating the region…

Q: The graph of the volume for solid revolution between the curves y = x+1 and y = O around the x -…

A: Plot the lines and determine the area bounded by these lines. Use the area and the rotation about…

Q: b) The area bound by the curve y = 2x + 1 and the y-axis is rotated about the y axis between y = 2…

A: We need to calculate the volume.

Q: Find the moments and center of mass for the thin plate covering the region between the x-axis and…

A:

Q: Find the volume of the solid of revolution obtained by revolving the region under the curve y = f(x)…

A: Use formula of volume revolved about x axis

Q: Find the volume of the solid generated by rotating the region bounded by the curves y = e^x and y =…

A: In the question we have to find the volume of region bounded by the given curves.

Q: Find the center of mass for the region bounded by y = 4 - x² that is in the first quadrant

A:

Q: Find the center of mass of a thin plate covering the region bounded by the curve y2 = 4ax and the…

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Q: Find the volume of the solid generated by revolving the region between the curves y af and y ya…

A:

Q: Find the volume of the solid of revolution obtained by revolving the region under the curve y = f(x)…

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

Q: Find the volume of the solid of revolution generated by revolving the region bounded by y = cos x, y…

A: By using the washer method we find the volume please see the explanation below

Q: Find the center of mass of a thin plate covering the region bounded below by the parabola y = x2 and…

A: Given:Find the center of mass of a thin plate covering the region bounded below by the parabola y =…

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Given, curves and lines are

Q: (b) Find the volume of the solid obtained by rotating the region bounded by the curve y=x²+x-2, y =…

A: Given is : The curves y=x2+x-2, y=0 The rotation is about the x-axis. We need to find the volume of…

Q: 4. Illustrate and find the center of mass and moment of inertia with respect to x and y for the…

A: y = f(x) =4-x2   only in First quadrant…

Q: Find the volume of the solid generated by revolving the region bounded by the curves y = 6 cos x; y…

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

Q: Find the center of the mass of a thin plate of constant density & covering the region bounded by the…

A:

Q: Consider the region bounded by the graphs of y = ln x, y = 0, and x = e. c. Find the volume of the…

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Q: 3. Find the volume of the solid formed by revolving the region formed by the curve y = sec about the…

A:

Q: Find the center of mass of the lamina bounded by the graphs of the equations x = 64-y² and x = 0 for…

A:

Q: find the volume of the solid obtained when the region under the curve y=1/(1+5x)^2 from 0 to 1 is…

A:

Q: 4- Find the volume of the solid obtained by rotating about the x-axis the region under the curve y =…

A: Given curve, y=5x from 0 to 4.

Q: Find the volume of the solid generated by revolving the region bounded by the curves y = 6 cos x: y…

A: we giveny=6 cos x, y=ex,x=0 ,x=π6 around the line y=7so, volume of the solid generated b revovlving…

Q: Compute the mass of the plate having density f(x, y) = 1 - y on a region D bounded by y = and x + 9y…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the curves y = 6 cos x; y…

A:

Q: Find the center of the mass of a thin plate of constant density & covering the 3 region bounded by…

A: Let thin plate is the region is bounded by two curves f(x) and g(x) on the interval [a,b] then…

Q: What is the volume of the solid rotated about the x-axis under the curve y = 2x -1 from x = 1 to x =…

A: Volume by disk method: The volume of a shaded region bounded by two curves over the interval [a,b]…

Q: Rotate the region specified above by the curve y = x and beneath by the curve y = x2 from x = 5 to x…

A: Explained below

Q: 2. Find the volume of the solid generated when the region between y = sin x and y = 0 for 0 ≤ x ≤ π…

A: The region between y=sin x and y=0 for 0≤x≤π is revolved about the y-axis.

Q: from

A:

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A:

Q: Find the volume of the body resulting from the rotation of the given region by the following…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the curve x = e^y2 y = 1…

A:

Q: Find the volume of the solid generated by rotating the region bounded by the curves y = e and y =…

A: We need to find the volume of the solid generated by rotating the region bounded by the curves y=ex…

Q: Find the volume of the solid generated by rotating the region bounded by y = sin²(x) and y = 0…

A:

Q: Find a curve such that when the portion of the curve from x = a to x = b is rotated around the…

A: Let the curve be y=fx.  The curve is rotated around X-axis from x=a to x=b.  The surface area of…

Q: Find the volume of the solid generated by rotating the region under the curve y=√x from x=0 to…

A:

Q: Find the center of the mass of a thin plate of constant density 6 covering the region bounded by the…

A:

Q: Find the center of mass of the region bounded by the curves y=4x-x2 and the x-axis

A: Center of mass is given by- x^=1A∫abfx-gxdxy^=12A∫abf2x-g2xdx Where  A=∫abfx-gxdx

Q: Find the volume of the solid of a revolution bounded by the graphs of f(x) = – x² + 5x – 4 and y = 0…

A:

Q: The volume of the solid that results when the region between the curve y=ex and the line y = 0, from…

A:

Q: Find the volume of the solid obtained by rotating about the x-axis the region under the curve y=…

A:

Q: Find the center of the mass of a thin plate of constant density ô covering the region 3 bounded by…

A:

Q: Find the volume V of the solid of revolution that results when the region under the graph of f(x) =…

A: To find the Volume V.  Given that f(x) = ln(x).

Q: Rotate the region specified above by the curve y = x and beneath by the curve y = x^2 from x = 0 to…

A:

Q: Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x…

A:

Q: Find the volume of the solid generated by rotating the region bounded by y = sin°(x) and y = 0…

A:

Q: Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x…

A: First find the intersection points of the given curve, by equating the y of both curves…

Q: Find the volume of the solid obtained by rotating about the x-axis the region under the curve y = /x…

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

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.