(b) Figure Q4(b) shows a region that bounded by the curve y=2x' – 4x² + 2 and line y=2 _y= 2 (2,2) 1.5 1 0.5 0.5 1.5 y=2x – 4x + 2 Figure 04(b): The shaded region bounded by the curve and line

Q: b) The region is between the curves y horizontal line y = 1. i, y = 1 and x = 0, above the x4 ,

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Q: find the center of mass of a thin plate of constantdensity d covering the given region. The region…

A:

Q: The area of the region bounded by the curves y =x and y = 20-x² is =J 120-x² -x| dr -5 попе 4.4 A =…

A: First find out the intersection points of both the curves than integrate.

Q: What is the volume of the solid that results when the region enclosed by the curves y = cosx and y =…

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Q: Region bounded by y = x* +2, y = x+4 rotated about the x-aKis 2.

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Q: Sketch the region bounded by the graphs of the functions. y = x2 – 8x + 16, y = x2 – 24x + 144, y =…

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Q: 2. Region bounded by y= x, x=0 and y=15, rotated about the y-axis

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Q: Describe the region R bounded by the curve y = x² and the line y = 2r in terms of inequalities using…

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Q: Compute area of the region bounded byx2+ (y−1)2= 9 andy=x+ 1 and the (horizontal) liney= 1 (we…

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Q: The area of the region bounded by the curves y=x and y= 20-x² is

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Q: Calculate the area of the plane region bounded by the function Y=X²-4X +5, and the line that passes…

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Q: The geometric center of the region bounded by the curves 5y²-16x=0 and y²+8x=24 on the first…

A: The given answers do not match the actual answer. Please check the options.

Q: Determine the area of the region bounded by 3x - 5y + 4 = 0 and y-axis from y = 2 to y = 5.

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Q: Find the line y=mx that divides the area under the curve y=x(1-x) over [0,1] into two regions of…

A: Given,           The line y = mx that divides the area under the curve y = x(1-x) over [0,1] into…

Q: What is the area of the region enclosed by the curves y=e^x, y=x^2-1 and the lines x=-1 and x=1?

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Q: Sketch the region bounded by the given curves, then find its area. y = 12 - 3x^2, y = 4 - x^2

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Q: 3 Find the abscissa of the centroid of the region between the parabola y = 9 − x2 and the line y…

A: Given :The parabola y=9-x2 and the line y=2-2x from x=0 to x=2.To find :The abscissa of the centroid…

Q: Find the line y = mx that divides the area under the curve y = x(1 − x) over [0, 1] into two regions…

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Q: 3. Region bounded by Y = rotated about the x-axis ,x=0 and y=15,

A: By shell method

Q: The area of the region bounded by the z-axis and the curve = ²t - 1, y = 1-t² equals to: [2(1-1²)e²…

A: Solution

Q: 4. Region bounded by y = x2, x=0 and y=15, rotated about the y-axis

A: Imagine the plot and rotate it about the axis specified and the resulting figure will lead to the…

Q: Find the area of the region between the curve y = 3 - x2 and the line y = -1 by integrating with…

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Q: 15. Find the area of the region enclosed by the curve x = y³ – y' and the line x = 2y. (Hint: Need…

A: We are asked to find the area of the region

Q: Find the area of the region bounded by the 3 graphs of the equations y = sin x, y = sin° x, 0, and x…

A: Consider the given curves. Equate (1) and (2) and calculate the x where (1) and (2) are equal.

Q: The bounded by y= xx*+1, area of the region axis. y=x, x-- 3, and

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Q: Find the area of teh region bounded by y=5x/x2+2, x=1, x=5, y=0. Sketch the graph

A: We graph the region using a graphing calculator.

Q: Sketch the region bounded by the graphs of the functions. y = x2 - 4x + 4, y = x2 - 12x + 36, y = 0

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Q: The area of the region completely bounded by the curve y = 23 the x-axis, and the line containing…

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Q: The line x=-3 of the region bounded by the 2x=4-y2 and 2x=y2-4 curves Calculate the volume of the…

A: We first sketch the region using a graphing calculator. 2x=4-y2 (red) 2x=y2-4 (blue) x=-3 (green)

Q: Sketch the region enclosed by the curves. x + y = 3, y + 3x = 3, x - y = 0 f(x) = + 10- -8-

A: Drawing the given line.

Q: The region is bounded by the curve y = 6x – x² and y = x² – 2x –

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The region is bounded by the curves y = x² and y = 4x - x² and is rotated about the line X = 4. %3D…

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Q: $ find the area of region in the first quadrant bounded on the left by the y-axis, below by curve x…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Sketch the region bounded by the curve y = x(x – 1) and the linear equatio x at (-1,2). Calculate…

A: Given: y=x(x-1)

Q: Find the area of the the Curves bounded region x +y=O by X+y² =2

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Q: 5. Find the area of the surface of revolution generated by revolving .3 y = on interval [0,3] about…

A: Given: The function y=x33on interval 0,3, To find: The area of the surface of revolution generated…

Q: A solid is obtained by rotating the shaded region about the specified line. about the line y = 5 y x…

A: NOTE: Refresh your page if you can't see any equations. . given functions are

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: 4. Region bounded by Y = x rotated about the y-axis ,x%30 and y=15,

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Q: Find the area of the = -, y=3-k| region that is restricted between is curves.

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Q: Sketch the region bounded by y =x² and x =y ( x 2 0) about the x-axis. %3D

A: Solve the following

Q: The area bounded by the curves y = 1 -x2 and y = - x2 + 2 x + 3 , line x = -1 and x = 1 is

A:

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given, y2=4-xx=0

Q: 0otained by rotating the region bounded by the given curves about the specified line y=x, y= 27, x-…

A:

Q: The region bounded by the curves y=1-x^3. ,y=e^x.  And the line y=3

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Q: Determine the area bounded by the curve y = x2 - 3x -6 and lines y =-4-x,x = 0 and x = -2.

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Q: The region is bounded by the curve y = 4x – x², y = 4 and the y-axis.

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Q: Sketch the region bounded by the graphs of the equations and find its area. y =x² +1; y=x+1

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.