Find the area between x = 1- y² and y = -x - 1. Sketch the region.

Q: Find the area of the region between y = x sinx and y = x for 0 ≤ x ≤ π/2.

A: We need to Find the area of the region between y = x sinx and y = x for 0 ≤ x ≤ π/2.

Q: problem in photo attached

A: Graph the functions. Shaded the bounded region by y=x^2 and y=x^4.

Q: Find the area between the curves. y = x2 - 18, y = x - 6

A: y = x2 - 18, y = x - 6

Q: Find the area between the curves. y = x2 and y = - x2+18.

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Q: find the area of the region enclosed by the curves y=x^2-2 and y=2

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Q: Find the area of the region bounded by y = ex and y = 12 − ex and the y-axis.

A: Given, y=exy=12-ex and the y-axis   Find the area bounded by the region:

Q: Find the area between the curve y=4x-x² and the x-axis

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Q: Find the area of the region under the curve y 3x +2x, the x-axis, x=0 and x 4. 0

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Q: Find the area bounded by the curve y = 8 – x and both coordinate axes in the first quadrant. Area of…

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Q: Estimate the area under the curve y=64-x^3 between x=0 and x=4. Use four rectangles

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Q: Find the area of the region enclosed by the curves y = |x² – 4[ and y = 4+

A: We sketch the region using a graphing calculator y=|x2-4| (green)  y=4+ x2/2 (violet)

Q: Find the area of the region between the curves 4x + y^2 = 12 and x =y.

A: 4x+y2=12    and  x=y

Q: Find the area of the region between the curves y = 1+ Væ and y = (3 + x)/3. Area between curves =

A: Firstly we find out the points of intersection, we put equation equal to each other , 1+x = 3+x/3 1…

Q: Find the area between x = y2, x - axis, x =y +2 To find the intersect points

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Q: Find the area of the region between the curves (x = y² ) and (x = y + 2 ) in the first quadrant.

A: The formula to find the area under the region between the curves is Area=∫y=ay=b[f1(y)-f2(y)]dy.…

Q: Find the area bounded by y =2x and y = 9x - x2. Sketch the region.

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Q: Find the area of the region that is enclosed between the curves y = x² and y = x + 6.

A: The given curves are, y=x2 and y=x+6. The objective is to find the area of the region that is…

Q: Find the exact area of the region that lies beneath the curve y = 8 sec2 (x), 0<x < n/3.

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Q: Find the area of the region bounded by the curves y = e", y = x e", and x = 0.

A: Given curves are y=ex, y=xex Point of intersection of the curves are evaluated as follows.…

Q: Find the area of the region enclosed by the line y = 4x and the curve y = x3 + 3x?

A: Given: y=4xy=x3+3x2

Q: Find the area of the region between the curves y = |x| and y = x² – 2. Area between curves =

A: Given : Two curves y = |x| and y = x² - 2

Q: Find the area bounded by the curves x 2 = y − 1 and = y − 3 .

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Q: Calculate the area between the curves y = 7- 2x2, y = x2 + 4, and the x-axis.

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Q: Find the area of the region between the curves y = x and y = x². Area between curves =

A: It is given that,  y1=x and y2=x2 Therefore,                    x2=x⇒x2-x=0⇒x(x-1)=0 ∴  x=0,1…

Q: Find the area of the region between the curves 4x + y = 12 and x Area between curves = %3D

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Q: Find the area between the curves y = x² + 1 and y = x + 1.

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Q: Find the area of the region between the curves y |Jx and y x2-2 | Area between curves

A: Given,

Q: Find the area of the region enclosed by the line y=4x and the curve y= x+ 3x.

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Q: Calculate the area of the region that lies under thecurve and above the  x-axis. y =1- x2

A: The graphical representation of the area is,

Q: Find the area of the region between the curves 4x + y = 12 and x = y. Area between curves

A: Solution

Q: Find the area bounded by the curves, y = 2x –x² and y=x-2.

A: Here we have to find the area bounded by the curves, y=2x-x2 and y=x-2 .

Q: Find the area of the region between the curves y = 12 – x and y = x* – 6. Area between curves =

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Q: Find the area between the curves x = 10 − y2 and y = x − 8

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Q: Find the area enclosed by the curves x = -2, x = 3, y = 3x2 - 70, and y = 12x + 26.

A: Consider the area enclosed by the curves x = -2, x = 3, y = 3x2 - 70, and y = 12x + 26.

Q: Find the area of the region between the curves x 2y and x + y = 1. Area between curves =

A: Given curves are x = 2y2  and x + y = 1 Here we have to find the area between the curves.

Q: Determine the area bounded by the curves y = -² – 20z + 96 and y= (r – 4)?.

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Q: Find the area of the region in the first quadrant that is enclosed by the curves x=y, y=x-, and the…

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Q: Find the area bounded by the indicated curves. y=7-7x2, y 0

A: We have to find out the area enclosed by the curves

Q: Find the area between the curves y = x and y = -x

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Q: Find the area of the region inside the circle x + y = 2 and above the line y = 1. %3D

A: We have above diagram from given statement and area of yellow part , we have to find We can see…

Q: Find the area of the region between the curves 4x + y = 12 and x = y. Area between curves =

A: R

Q: Find the area of the region in the second quadrant bounded by y= -x and y=x^4

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Q: Find the area of the region between the curves y = x² and y = x. Area between curves =

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Sketch the region below the curve y = x – x² and above the x-axis and find its area.

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Q: Find the area of the region bounded by y = 7x + 7, y = -9x + 4 and x = 15. Leave your answer correct…

A: The solution of the problem is given in the next steps.

Q: Find the area of the region enclosed by the curves: y =x', and y= 2x-x

A: Consider the curves  y=x2y=2x−x2

Q: Find the area bounded by the curve y = 4x - x² and y = 3. Answer:

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Q: . Calculate the area bounded by the curve y= 4(x – 1) and the x -axis. A)

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Q: Find the area bounded by the curve y = ex, the lines x = -1, x =1 and the x axis.

A: To find the area bounded by curve y = ex, the line x = -1, x = 1 and the x-axis

Q: Find the area of the region bounded by y = 4x + 6, y = -3x +1 and x = 15. Leave your answer correct…

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.