Find the volume of the region bounded by the curve x=y2 , x = 0 and y=14 by using shell method

Q: Draw the area bounded by function y = x^2 + 1 and line y = 5, then calculate the volume of the solid…

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Q: Find the volume of solid formed when the region bounded by y = x* and y = VE revolved about the are…

A: Consider the provided question, The region bounded by the given curve is shown as,

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

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

A: We have to solve the given problem.

Q: Q2 a) Find the total area of the region enclosed by the curves in below figure: (-2,8) y-axis (2,8)…

A: Given problem is :

Q: Find the area of the region bounded by the curve y=x^2−1 and the line y=15.

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Q: The line y= X+2 and the curve y= x contain bounded region between them. Find the volume of the solid…

A: The volume for solid of revolution between curves is the volume of object between a curve f(x) and a…

Q: Find the volume of the solid formed by revolving the region bounded by the graphs y = √x and y = x^2…

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Q: A body T with the parameters  (1/2)(sqrt(x^2)+(y^2))≤z≤sqrt(16-(x^2)-(y^2) Use the sphere…

A: The given problem is to find the volume of the body formed by the cone and spherical region, we have…

Q: Find the centroid of the volume generated by revolving about the line x = 1, the area bounded by x2-…

A: We will use basic integral calculus and techniques of integration to answer this question.

Q: Find the volume of the solid bounded by the cylinders x² + z² = 1 and y² + z² = 1.

A: The given problem is to find the volume of the solid bounded by the given cylinders x2+z2=1 and…

Q: Find the area and centroid bounded by y=-x^2+6, y=x^2+3x. Graph

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Q: The area enclosed by y = 4x - x^2 and 2y = 2x + x^2 is revolved about the line x = -1. Using a…

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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.