Find the areas of the regions enclosed by the lines and curves in Exercises 75–78. 75. x = 2y2, x = 0, and y = 3 76. x = y2 and x = y + 2 77. y2 - 4x = 4 and 4x - y = 16 78. x - y2 = 0 and x + 2y2 = 3

Q: Region inside the circle(rz1)_and outsid the cardiaid (1- Cuso).

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Q: Find the area of the region bounded by the curve  y=2x2-3x+2  x axis and vertical lines x=0 and x =…

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Q: Sketch the region bounded by the graphs of the equations (include representative rectangle) f (y) =…

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

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Q: Find the area between the curves.

A: First sketch the region bounded by the curves x=1,  x=6,  y=1x  and  y=12 as shown below.

Q: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

A: the area is given by  A=∫ab|fx|dx................(1) here we have fx=3xex2 the upper and lower limit…

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

A: 4x+ y2 = 12, x = y We need to find the area of the region bounded by the curves.

Q: Find the area bounded by the curve y=1/x and the lines 2x-y=0, x=6 and the x-axis

A: Given the region is bounded by the curve y=1x and the lines 2x-y=0, x=6 and the x-axis.

Q: 2. Can you make a conformal map that maps the region bounded by |z + 1| = 1 and |z| = 2 to the…

A: Given: |z+1|=1 |z|=2

Q: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

A: We have to find the total area of the region bounded by the curve y=x, the x-axis y=0, and the lines…

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

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

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Q: Find the areas of the regions enclosed by the curves in Exercises 83–86. 83. 4x2 + y = 4 and x4 - y…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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: Find the areas of the regions enclosed by the curves in Exercises 81–84. 81. 4x2 + y = 4 and x* - y…

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

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Q: Find the area of the region bounded by the curves 1 y = (x+6)²¹ Y = 4 and the x-axis using vertical…

A: Given problem is :

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

A: Given, y=2x+1y=12-x2x=-1x=2 graph for the given problem is :

Q: Sketch the region enclosed by the curves y=x+2, y=25-x^2, x=-2, and x=2. Find the area of the…

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Q: What is the area of the region enclosed by the curve y=x^2 and the lines y=x+6, x=0 and x=5?

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Q: Sketch the region enclosed by the curves and find its area. 1 y = 6x² ,y = 6/x, x =-andx = 1 Enter…

A: The region enclosed by the curves,y=6x2, y=6x, x=14, x=1

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

A: We sketch the region using a graphing calculator.  This is same as:

Q: Find the centroid of the region bounded by the graphs of y = x² and x + y = 506. NOTE: Enter the…

A: Centroid of the region y=f(x) and y=g(x) on [a,b] :            x¯ = 1A ∫ab xfx-gx dx  and   y¯ =…

Q: Determine the area of the region bounded by y = xe¯x² , y = x + 1,x = 1, and the y-axis. %3D

A: Given  y=xe-x2y=x+1x=1x=0  i.e. y axis

Q: Find the area :  The curve y=4x-x2 and the lines y=0, x=1 and x=3.

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Q: Sketch the region enclosed by the curves/lines x = y, y =1/x, x = 3 and find its area.

A: given,         x=yy=1/xx=3

Q: 3. Explain how we know that it is possible to cut a surface with continuous boundaries in exactly…

A: We should mathematically establish the possibility of cutting a surface with continuous boundaries…

Q: Find the area of the region grapa) enclosed by the curves y= x* - 2 ( show y =2

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Q: Find the area of the region bounded by the curve y = x³ and the lines y = -x, y = 1. (Draw the…

A: The region is bounded by the curve y = x3 and the lines y = -x , y = 1. The region is drawn in the…

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

A: Given:

Q: Sketch the region enclosed by the curves y = 5x and y = 5x2. List the points of intersection of…

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

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Q: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

A: Our objective is to find total area of the region bounded by y=2x,the x-axis,and the lines x=2 and…

Q: Sketch and find the area of the region below the interval -3, -2 and above the | curve y = . Area…

A: An interval is given by -3,-2 and a curve is given by, y=x34  . The objective is to sketch and find…

Q: Find the area R -region bounded by the curve y=1/x^2 and the lines y=x and y=x/8.

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Q: Sketch the entire region bounded between the curves, x=y^2 and y^2 =x-4. Determine their…

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Q: What is the area bounded by the curves y=x2+5 and y=−x2, the line x=3, and the y axis.

A: Given that, The curves are y=x2+5 and y=-x2, the line x=3, and the y-axis. Find the area bounded by…

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

A: Given equations y=5/x, y=5/x^2, x=3 , following is the correct graph:

Q: Determine the area of the region enclosed by the curve y = x2 – 2 and line y=2

A: Given that y=x2-2 and y=2To determine the area enclosed by the curve.Solution:

Q: Find the areas of the regions enclosed by the curves and lines √x + √y = 1, x = 0, y = 0

A: To Find: Area of the regions enclosed by the curves and the lines x+y=1, x=0, y=0. Concept: AreaA…

Q: 8. Sketch the curves and determine the area of the region formed in the given interval: y = √√2x, y…

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Q: Determine the area enclosed by the curves y =-x + 4x and y =-x+4. Draw a sketch of the graphs on the…

A: The shaded region represents the region enclosed by the given two curves.

Q: Find the area bounded by the given curve and lines. y = x3,y = 8, and x = 0 %3D

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

A: The formula for the area of the region bounded between the two curves is A=∫x1x2[f(x)-g(x)]dx, where…

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: Find the areas of the regions enclosed by the curves and lines x = 4 - y2, x = 0

A: The area of the regions enclosed by the given curve x=4-y2 and the line x=0 is shown in the figure…

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

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Q: 23.a) determine the area of the region bounded by x= -y²-3 and x= (y – 2)2 ? (Sketch the region)

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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.