Find the volume generated by the revolving the region bounded by y = x, and the lines y = 3, and x = 1. a. about the line x = -2 b. about the line y = -2 + 2

Q: Determine the volume of the rotating object that occurs if the area of ​​the curve y1 = - x2 + 4 and…

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Q: Find the area of the plane region bounded by y=-x+2 and y=x²-2x 07 s.u. 9 9 s.u. 01 S.U. 2 S.U.

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Q: Revolve the region between y=x-x4 and y=0 about the y-axis. Find area

A: The given region is between y=x-x4 and y=0 and it is revolved around y- axis.

Q: Find the aren of the region in the tirst quadrant baunded by the line y=27, e the line X-4, the…

A: We first sketch the region using a graphing calculator.

Q: Find the area of the surface obtained by rotating the line y = 19x + 6 about the x - axis from the…

A: Area of surface is evaluated.

Q: 3) Find the volume of the first quadrant region bounded by y = x² , the y-axis and y = 4 rotated…

A: Please refer the attached image for complete solution.

Q: Let R be region bounded by curves y = x2-1, y = - x2+7 and straight lines x=-1 and x=3. GRAPH R and…

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Q: Find the center of mass of a thin plate of constant density 8 covering the given region. The region…

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Q: Find the AREA and VOLUME (Identify what type of volume) bounded by the equations; y = 4x - x² and x…

A: The given curves are y=4x-x2 and x+y=4 We have to find the area and the volume bounded by these…

Q: Find the area of the region between the curves y = x + 1, y = 9 – x², x = -1, and x :2. %3D Area…

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Q: A rectangle has side lengths 5 cm and 12 cm. What would the side lengths of the image be after a…

A: Given the rectangle with  length (AB)=12cm breadth BC=5 cm scale factor is given as 35 clearly the…

Q: Find the area of the region bounded by the curve y =1-- 2 and the x-axis. O 8 square units square…

A: Put y=0 to obtain the x intercepts. 1-x29=0x2=9x=±3

Q: The area of the region enclosed by the parabola y = x - 6 and the line y = x.

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Q: Find the area bounded by the parabola x=8+2y-y², the y-axis, y=-1, and y=3 A 92/6 s.u. B 92/4 s.u.…

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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.