/ The volume generated by rotating the region bounded by the given curves y = v-x +1+ 2, y 2x, y = 0, x = -3 about x=-5.

Q: Find the volume of the figured form by rotation f(x) = 1 + 2x^2 around the line y = 5 on the…

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Q: Determine, with justification, whether the series converges absolutely, converges conditionally, or…

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Q: Find the volume of the solid that sits above the rectangle [−1, 1]×[0, 1] in the xy-plane and below…

A: Given: Rectangle [−1, 1]×[0, 1] in the xy-plane Surface z = x^(2/3)+y^(1/3)

Q: Find the volume of the region bounded by y=x^2 Below the x axis And on the right by the line x=3…

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Q: Find the centroid of the region in the plane enclosed by the curves y = +-(1 - x2)^(-1/2) and the…

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Q: Find the area and centroid bounded by y= 2(1-x^2), y=x^2-1. Graph.

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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: Set up an intergral for the volume of the solid obtained by rotating the region bounded by the given…

A: Use the method of cylindrical shells. The graph of the bounded region is given below.

Q: Find the volume of the region bounded by y=x^3 and y=x rotated about the x-axis.

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Q: Find the area of ​​the region bounded by the curve x = 2y², the line 2y = x - 4 and line tangent to…

A: We need to find point of intersection to draw the graph and identify  region bounded by them ; Then…

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.