Find the volume V of the described solid S. The base of a solid S is the region enclosed by the parabola y = 4 - x and the x-axis. Cross-sections perpendicular to the y-axis are squares. V =

Q: The base of a certain solid is the triangle with vertices at (-6, 3), (3, 3), and the origin.…

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Q: The square region with vertices (15,0), (30,15). (15,30), and (0,15) is revolved about the x-axis to…

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Q: Find the function f(x) described by the given initial value problem. f"(x) = 3 sin x, f'æ) = 3, f(1)…

A: The objective is to find f(x), find the area of the region encloses by the parabola and the x-axis.

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: Find the volume V of the described solid S. The base of S is the region enclosed by the parabola y =…

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Q: The graph of the derivative f'(x) of f(x) is shown. Compute the total change of f(x) over the given…

A: Graph of f'(x) vs x is given. Here, f'(x)=∆f∆x Therefore, change in f(x) will be, ∆f=f'(x)·∆x It…

Q: A pontoon is to be made in the shape shown. The pontoon is designed by rotating the graph of…

A: Given: y=1-x216; -4≤x≤4. We have to find the volume of the pontoon obtained by rotating about the…

Q: The base of a solid is the region bounded by the x-axis and the graph of y = v1 – x². For the solid,…

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Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: Given that  Plane x+7y+10z=70  To find the largest volume

Q: A solid lies between planes perpendicular to the x-axis at x = 0 and x = 19. The cross-sections…

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Q: Find the volume V of the described solid S. The base of S is the region enclosed by the parabola y =…

A:

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.