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: 2. a) Find the area of the region bounded above by y= ex, bounded below by y=x and bounded on the…

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Q: Write the equation for the volume obtained by rotating the region shaded below about the line y =…

A: Hee, the volume formula is: V=π∫ab((f(x)-a)2-(g(x)-a)2) dx where the region bounded by the curves…

Q: a. x = 2y, y = 2 and y= 3; revolved about x-axis 4. (0, 3) y=3 (0, 2 y=2 -2. -4. 0 x=0 x = 2y + 2.…

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Q: The semicircular region bounded by the curve x = √9 - y² and the y-axis, is revolved about the line…

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Q: W 106° U ? V

A: To find the measure of unknown angle m∠UVW.

Q: 4. Consider the rectangle bounded by x = 1 and x = 4 on the y-interval [3, 3.5]. (a) What is the…

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Q: What is the volume (in πcu. units) of the region bounded by the curve y=x^3, and the lines x=1, x=2…

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Q: 17) Find the total areas of the regions bounded 17.1) y = e", y = e(2 – x), y axis |

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Q: Find the volume of the solid of revolution generated by revolving the region in the first quadrant…

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Q: Let be the region bounded on the left by the right branch of the hyperbola 2- = 1, on the right by…

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Q: Use the best method available to find the volume. The region bounded by y =x and y =x - 42 revolved…

A: We need to find the volume for region bounded by y=x and y=x2-42 revolved about y=-42. Draw the…

Q: The portion of the y=-3*x^2+3 curve in region 2 of the analytical plane. What is the volume, in…

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Q: Which of the following is the volume of the object formed by the rotation of the region bounded by…

A: We first sketch the region using a graphing calculator  The shaded region will rotate about the y…

Q: Find the volume generated revolved about when the area of the curve the line y=-4 x² = -y is

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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.