Find the volume of The region R bounded by the graph of y=4sinx and the​ x-axis on [0, π] is revolved about the line y=−5.

Q: Find the volume of the solid obtained by rotating the region under the graph of the function…

A: We first sketch the region using a graphing calculator  The shaded region will rotate about the…

Q: Let M be the region in the first quadrant bounded by the graph of y=3x+2, the graph of y=x+2, and…

A:

Q: Find the volume of the solid that results when the region bounded by x = y and x = y + 12 is…

A:

Q: Consider the region formed by the graphs of f (x)=sqrt( x) , f (x)= 1/x and x = 2. Set up the…

A: We sketch the region using a graphing calculator.  Red curve is : y=1/x Violet curve is: y=sqrt(x)…

Q: Consider the region formed by the graphs of f (x)=sqrt( x) , f (x)= (1 /x)and x = 2. set up the…

A: We sketch the region using a graphing calculator. Violet curve is: f(x)=sqrt(x) Black curve is:…

Q: Find the volume of the region that results when the region bounded by the curve x=y^3 and the line…

A: Find the cross sectional area and use it to find the volume.

Q: 2. Find the volume of the region bounded by y = vx and y 4x rotated about the x-axis.

A:

Q: Find the volume of the solid obtained when the region bounded by the curves y = x^4 − 2x and y = 0…

A: We have to find the volume of of the solid of revolution of the region bounded by the curves y=x4-2x…

Q: Find the volume of the solid generated by the area bounded by the curve y = x³,x = 1,x = 2 and y = x…

A: The volume of a region is the integration of the area of the region. It can be calculated using…

Q: 2. Find the volume of the solid obtained when the region between the graph the y = f (x) = Vĩ and y…

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Q: Find the volume of the solid generated when the region bounded by x = - sqrt(4y) . y = 4 and x= 0 is…

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Q: 4. Find the volume of the region bounded by y = -x+1, x = 0 and y = 0 revolved about the x-axis.

A:

Q: , Find the volume of the solid. The region bounded by y = 2x – x? and y = x about a. The y - axis b.…

A: a We have to find the volume of the solid      bounded by y = 2x-x2 and y=x about y-axisFor point of…

Q: sketch the solid obtained by rotating the region underneath the graph of the function overthe given…

A:

Q: What is the volume of the region bounded by the lines f (x) = x²,x = 2, and y 49 rotated about the…

A: Given data:     The given equation is: f(x)=x2. The second equation is: x=2. The third equation is:…

Q: Find the volume of the solid whose base is the region bounded between the curve y = x2 and the…

A: Given that the solid whose base is the region bounded between the curve y = x^2 and the x-axis from…

Q: Find the volume swept out by revolving the region bounded by the y-axis and the graph of x = t (1 -…

A: Given,

Q: Consider the region bounded by the graph of y2 = (6 – x)2 (1 + x)2 on the interval [o, 1]. Find the…

A: Given: y2=6-x21+x2 To Find: The volume of the solid generated by revolving the region about the…

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: Find the volume (in cubic units) of the region bounded by the curves (y – 1)° = x – 1 ,and the lines…

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Q: Find the volume of the area bounded by the line y = 3x + 4 and the curve y = x² if it is revolved…

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Q: 4. Find the volume of the region bounded by y = - x+1, x = 0 and y = 0 revolved about the x-axis.

A:

Q: sketch the solid obtained by rotating the region underneath the graph of the function overthe given…

A: The volume of the function, f(x) about y axis in the interval [a,b] is given as,

Q: Find the volume of a solid of revolution formed by revolving the region bounded by the graphs of…

A: The objective is to find the volume of a solid generated by revolving the region bounded by the…

Q: 2. Find the volume of the region bounded by y = x3 and y = x rotated about %3D the x-axis.

A: In this problem we can use washer method to find the volume of the solid of revolution. Washer…

Q: Find the volume of the solid obtained when the region under the curve y = x/4 – x2 from x = 0 to x =…

A: Given data:     The given expression is: y=x(4-x2)1⁄2. The given limits of x is: (a,b)=(0,2). The…

Q: Find the volume of the solid obtained by rotating the region under the graph of f (x) = 9 − x2 for 0…

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Q: The region R bounded by y=x^(1/2) +2 and y=x2+2 in the first quadrant is revolved about the line…

A: The given equations are

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

A:

Q: Find the volume of the solid obtained by rotating the region under the graph of the function f(x) =…

A: We will  use concept of integration to solve this. In particular disc method  will be used.

Q: Find the volume generated when the area bounded by the two curves of x^2 = 4y and y^2 = 4x is…

A: We will find out volume of solid of revolution.

Q: Find the volume of the solid obtained if the region bounded by the graphs of y = \x , y =0, and x=9…

A: Hello. Since your question has multiple parts, we will solve the first question for you. If you want…

Q: Find the volume of the solid whose base is the region bounded by the x-axis and the curve y=e^x…

A: It's given that each cross section perpendicular to the x-axis is a semicircle. Hence area of one…

Q: Find the volume of: the area bounded by the curve y2 = 9x and the line x = 4 revolved about x = 4.

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Q: Find the volume generated by the region bounded by the curve y 12X and the line X3 rotated about the…

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Q: Define R as the region bounded above by the graph of f(x) = 3x - x² and below by the x-axis over the…

A: To find the volume of the solid of revolution formed by revolving R around the y-axis .

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

A: The graph is where red curve represents y=x and blue line represents y=x.

Q: Let B be the region in the x y plane enclosed by y = 3−x2 and the x-axis. Let S be the solid shape…

A: let B be the region in x-yplane enclosed by y=3-x2 and the x-axis. S be the solid with base B and…

Q: The area bounded by y = x3 + 2x + 1, x = 1 and x = 3 is to be revolved about the x-axis. Find the…

A: Given problem:- The area bounded by y = x3 + 2x + 1, x = 1 and x = 3 is to be revolved about the…

Q: The region bounded by the curves y = x² – 2x and y = 4x is revolved about the line y = -1. Which…

A: The given curve is y=x2-2x and y=4x. Now, find the intersection point of these two curves.…

Q: 3. Find the volume generated when the region defined by y = x, y = 2x/(1+ x³) is revolved around the…

A: NOTE : As per Bartleby rules incase of multiple questions only one is answered. Please upload others…

Q: Consider the region bounded by the graphs of y = x√(16 − x2) , y = 0, x = 0, and x = 4. Find the…

A: Shell method: The volume of a solid generated by the region on [a, b] revolved about y axis is,…

Q: The region R in the first quadrant is bounded by y=(5x-4)^(1/2), y=0, y=4, and x=0 is revolved about…

A: Given,

Q: Find the volume of the solid obtained by rotating the region under the graph of the function…

A: volume is 76.9858 detailed solution with explanation is given below

Q: Find the volume of the solid obtained when the region enclosed by the curve x=2-y² and find the x=y…

A: Draw the sketch of the given curve and lines.

Q: find the volume of the solid obtained by rotating the region enclosed by the graphs aboutthe y-axis…

A:

Q: 2. Find the volume of the solid generated by revolving the region bounded by the y = ³, y= 0 and x =…

A: Find the volume of the solid generated by revolving the region bounded by the y=x3, y=0 and x=1…

Q: Find the exact volume generated by revolving the region bounded by f(x) = 2x^2 + 10 and g(x) = 4x +…

A: The volume generated by revolving the region by line y= 10 The given functions are fx=2x2+10 and…

Q: sketch the solid obtained by rotating the region underneath the graph of the function overthe given…

A:

Q: Find the volume of the region bounded by y= √x and y=4x rotated about the y-axis.

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.