Use the washer method to find the volume of the solid generated by revolving the shaded region about the x-axis. y#2 =X 2 -1/2 1/2 (Type an exact answer, using n as needed.) 9. xp (っ7 5

Q: Please see the picture below for the question. Thank you

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Q: Consider the solid whose base is the region bounded by the x-axis, y = x, and y=-4x + 5. Find the…

A: Sol:- To find the volume of the solid using the given method, we can integrate the area of each…

Q: b. y = 3x² −3,−2 ≤ x ≤ 2

A: The area between a curve f(x) and x-axis in the interval [a,b] is given by Formulas we use

Q: Find the area of the shaded region on the right. y = 4x² y = 6- 2x

A: Here, the intersection point of the given curves y=4x2,y=6-2x is at (1,4) from the graph.

Q: EXAMPLE Find the volume of the "ice cream cone" D cut from the solid sphere p< 1 by the cone o TT/3.

A: Volume is a quantity that measure the amount of space inside the solid in 3-dimensions. Volume of…

Q: Find the area of the shaded region. 1(1, 1) 5 10 y=√x y = 15 20 X = 27 25 X

A: The region bounded by curves  and  The given graph

Q: Find the area of the region between the parabola y = 9 - x2 and the x-axis. Round your answer to…

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Q: y=x? y=4x-x² 4 > 2 -2 -4 -1 1 3

A: Here we will find the area between the curves,

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.