A region in the xy-plane is bounded by y = 2x + 2, X = y + 2, y = -2, 2 y = 2. and

Q: Let R be the region bounded by the curve y = r and the line y = 2x. Use inequal- ities to describe R…

A: In this question we have to describe the area of region by using vertical cross section

Q: Find the area of the “triangular” region in the xy-plane that is bounded on the right by the…

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Q: Where is the centroid of the region bounded by y = 4-x2 and the x-axis?

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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: Find the three areas of the region bounded by y=2x^2+10, y=4x+16 and the lines x=-2 and x=5.

A: Given: y=2x2+10y=4x+16x=−2x=5

Q: Find the centroid of the region bounded by y = 9 – x² and the x-axis.

A: Given, y=9-x2or let fx=9-x2and x-axis y=0or let gx=0

Q: Sketch the region in the xy-plane defined by the inequalities x- 4y 0, 2- x - 7lyl 20 and find its…

A: Given region are   x-4y2≥0 and 2-x-7|y|≥0

Q: Find the centroid of the region bounded by the given curves y=8sin 5x, y=0, x=0,x=  π/5

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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: The area of the region enclosed by the curve 4x2+25y²=50 is:

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Q: Sketch the region in the xy-plane defined by the inequalities x - 2y2 ≥ 0,   1 - x -| y| ≥ 0, and…

A: Now the graph is,

Q: Sketch the region bounded by the graphs of y = 9- and y = 6- x, then find its area. 2

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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: 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 out the final coordinates of a figure bounded by the coordinates (1,1), (3,4), (5,7) and (10,3)…

A: Given that: Scaling factor Sx = 2 and Sy = 3 Assume that x and y are the original coordinate.…

Q: Find the number  b such that the line  y = b divides theregion bounded by the curves y = x 2  and y…

A: Given Data The equation of curve is y=x2. The equation of line is y=4. The equation of another line…

Q: Find the centroid of the region bounded by the set of curves y = 2x? + 10 ,y = 4x + 16 ,x =-2,and x…

A: Given

Q: . The solid bounded by z = 1 – x², z = 5 – 2x², y = 0, and y – z = 6. |

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Q: The region R is bounded by y 4 %3D and y = x +3. -

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Q: 1.) Find the area of the region bounded by the curve ya 12 and the lines y=o, y=x, x=2.

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Q: Find the volume of the region bounded by z = 4 - x² - y and the xy plane.

A: Given the region bounded by z=4-x2-y2 and the XY plane

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: rotate the region bounded by y=2x+1, x=4 and y=3 about the line x=-4

A: Solution:-

Q: Find the number 6 such that the line y = 6 divides the region bounded by the curves y = x2 and y =…

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Q: he region bounded by x2 + y2 = 4?, 4y = -5x and 13y = 6x where y 2 0. Leave your answer correct…

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Q: Evaluate the integral hipxp hx^ 7 and the hyperbola ry = 13. where R is the region bounded by the…

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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: Find the area of the region bounded by y = 5-x2, y 2x+2, y=-x-1, a. in terms of x b. in terms of y y…

A: We will find out the required value.

Q: Find the area and centroid bounded by 2x^2+4x+y=0 , y=2x. Graph

A: The region bounded by the curves 2x2+4x+y=0 & y=2x is as shown below.

Q: Find the three areas of the region bounded by y= 2x2+10, y=4x+1 and the lines x=-2 and x=5.

A: Given: y=2x2+10y=4x+1x=-2x=5……1   To find: Area of the region enclosed with the above curve and…

Q: Find the centroid of the region bounded by the graphs of the inequalities

A: Given information: y≤14x2          ...(1)x-42+y2≤16              ...(2)y≥0                ...(3)

Q: Find the area of the region cut from the plane x + 2y + 2z = 5 by the cylinder whose walls are x =…

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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: How would I go about solving ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2…

A: We will find out the limits first.

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: While evaluating the area of the region bounded by two curves y√=xy=x and y−15x+54=0y−15x+54=0, the…

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Q: It is possible for a region in the xy-plane to be both type 1 and type 2 at the same time.

A: This is possible.

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

A: Given,    y = x,  y = 4  and  x = 0 So the region bounded by these curves is given by shaded region…

Q: Sketch the region bounded by 1 + 2, y = -x, x= 1, x = 2 y = - %3D and FIND its area.

A: To sketch: the region bounded by the curves: y=1x+2, y=x2, x=1, x=2. And also, we need to find the…

Q: R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

A: Given regions are, y=x2y=4x-x2y=0 Now, using Washer method by the formula, V=π∫abR2-r2dx

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

A: Given: y = 9 - x2,  y = 0 To find: The value of b such that the line y = b divides the region…

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

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Q: Consider the region in the first quadrant bounded by y=x^2, the y-axis, and y=4. -the y-axis using…

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Q: Define the region bounded by y = 0, y=4Vx , y = 24 - 2x and y = X -4 using vertical and horizontal…

A: The equations of the bounding sections are: y=0y=4xy=24-2xy=x-4 The equations are plotted on a…

Q: Find the centroid of the region bounded by the graphs of the equations using any method y = √(1 −…

A: Consider the given equations y=fx=1-x2y=gx=0 First, find the point of intersection of the given…

Q: he volume bounded by y = x², y = 0 and x = 2 rotated about the specified = specified orientation of…

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Q: 2. Determine the centroid of the area bounded by the curves y = 4x + 16, x = -2, x = 5 and x-axis.

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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: Find the area of the plane region bounded by y=-x+2 and y=x²-2x

A: The given curves are y=-x+2 and y=x2-2x. The main objective is to find the area of the plane region…

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.