Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer for y = x^3, y=1, x=2; about y=-3

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: Consider the region R determined by the lines x=0, y=1 and the curve y=x^8. Determine n such that…

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Q: Find the surface area of the region formed by the portion af the plane y+z= 10 inside the cylinder +…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: Here in the given graph, upper graph of the function is y = 2x and lower graph of the function is…

Q: Find the center of mass of a thin plate of constant density 6 covering the given region. The region…

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Q: Determine the volume of the solid formed when a circle that passes through the points (l , 3), (3 ,…

A: As per the question we are given a circle passing through the three points : (1, 3) ; (3, 1) ; (1,…

Q: A thin metal plate of uniform density covers the area between the curves y = 2+ 6x – x² and y = 2 –…

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: Given curves are  4x-y=0⇒y=4xy=x2

Q: (a) Between 1 and the disk x²+ (1+x² +y*) (b) Between % = 1 and the entire xy-plane. (1+x* + y?)*

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Q: sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y.…

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

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Q: Q. Sketch the region enclosed by the curves y=2x^2 and y=2x. Find the volume of the solid when 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.