Find the area between the curve y = 4 – x² and the line y = -x + 2.

Q: Find the area between the curves y=e^−0.7x and y=2.1x+1 from x=0 to x=1. Area=_____

A: Using Formula of Area between two curves.

Q: Find the area between the curves y – 0.5x = e and y = 2.1x + 1 from x=0 to x=3 Area

A: Explanation of the answer is as follows

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

A:

Q: Find the area of the region between the line y = 2x and the curve y = x²+ x – 2

A: y=2x --------(1) y=x2+x-2 -------(2) For points of intersection…

Q: x = y² and the line y = x − 2

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Q: Find the area bounded by the curve x^2 + 4y - 8 = 0, the x - axis, and the lines x = 3 and = 5

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

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Q: Find the area between the curve y=x^3 and its tangent through (1,1)

A: The slope of the tangent is given by y' at (x,y)=(1,1) y'=3x2At x=1y'=3 Equation of tangent line is…

Q: What is the area bounded by the curve x^2 = -9y and the line y + 1 = 0?

A: Solution:Givenx2=-9yy+1=0To find the area bounded by the curveFormula:Area=∫abf(x)-g(x)dx

Q: Find the area A between the curves y=1+x² y=3+x

A:

Q: Find the area between the curves y and y 3x + 2.

A: From y=x3, y=3x+2 solving for the points of intersections.…

Q: Find the area of the curve y = x° – 2x – 3 between x =- 1 to x = 3.

A:

Q: find the area between the curves 2x^2+4x+y=0 and y=2x

A: Given that: 2x2+4x+y=0    and   y=2x

Q: Find the area between the two curves on [2,3]. y = ex y = (1/x)

A:

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: Find the area bounded by the curve y^2+x-4y=5 and the y-axis

A: Given: curve is y2+x-4y=5

Q: Find the area between the curve  y = x2 + 3  and the line  y = 2x − 2  (shown below) from x = 0 to…

A: We first sketch the area using a graphing calculator

Q: Find the area contained between the two curves y = 3x - 2² and y=x+x².

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Q: Find the area between the two curves: y = x2 and y = 4x + 5

A: In this question we have to find Area.

Q: Calculate the area enclosed between the x-axis and the curve y = x2 - 1 between x = -2 and x = 2.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the area between the two Curves- y=x, a°y = x³ 3,

A:

Q: Find the area between the curve y = sin 2x and y = x^2

A: the area is 4/5

Q: Find the area between the two curves y = x^2 and y = 2x – x^2

A: Given:     To determine: The area between the two curves.

Q: Find the area between the curves. x = -2, x = 4, y = 3e3x, y = 2e3x + 1

A: The above question is from the application of the integration part and since the major part of…

Q: Find the area between two curves f(x) = x² + 3x and g(x) = 6x.

A: The region bounded between the curves fx=x2+3x and gx=6x

Q: Find the area between the curve y = x – and y = -x + 10x2 – 24x 10x + 24x

A:

Q: Find the area between the curve y = sin x and the line segment joining the points (0, 0) and (5π/6,…

A: Consider: y=sin x and line joining the points 0,0 and 5π6,12. Find the area between them.   First…

Q: Find the area bounded by the curve y = 3x – x3 and the line y = 2

A: Given: y= 3x-x3; y=2 If f(x)> g(x) in the interval x=a to x=b, then the area between two curves…

Q: Find the area between the curves: y2=x x2– 2x + 3y = 2

A: we have to find the area between the curves :

Q: Find the area between the curve y=2x+4x-6 and the x-axis from x =-2 to x= 3.

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Q: Find the area between the curve inclosed by the curve x = 2y^2 and the curve x = 4 + y^2

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Q: Find the area between the curves. y = x4/3, y = 2x1/3

A: y = x4/3, y = 2x1/3

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 between the curves x=y² –1 and x = 2y² – 2.

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Q: Find the area above the curve y=lnx in the lower half-plane between x=0 and x=1.

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Q: Find the area between the curves y = e 1. = y = 2.3x + 1 from x = 0 to x = Area -0.4x and

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

A:

Q: Find the area between the curves: y=x^3-11x^2+18x and y = -x^3+11x^2-18x

A: y=x3-11x2+18x and y=-x3+11x2-18xTo find the area between the curves:

Q: Find the area between the curves: y=x^3−10x^2+21xx and y=−x^3+10x^2−21x

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Q: Find the area of the region between the line y = 2x and the curve y = x2 + x − 2

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Q: Find the area between the curves y = e – 0.4x and y = 2.1x + 1 from x = 0 to x = 4. Area =

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Q: Find the area between the curves y = x² + 5x and y = 3– x² between a = -2 %3D and z = 0.

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Q: Find the area between the curves y = 4x – 3 and y = x². %3D

A: Given data is : y=4x-3     .....1 y=x2      .....2 From equation (1) and (2) ,…

Q: Find the area between the two curves y = 3 y = x² – 1 1+ x2'

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Q: y = 3x2, y = 0 and x 31

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Q: Find the area between the curve y = 1/x7/6 and the x-axis from x = 1 to ∞

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

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Q: Find the area between the curve y = cos (2x) and the line joining the points (,0) and (등, 글).

A: Integrals and derivatives are considered as the inverses of each other. For example if we have a…

Q: Find the area bounded by the curve x^2=4y+4 and the line y=x+2

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.