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

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 = x2 and y = - x2+18.

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Q: Find the area bounded by the curve x = y² + 2y and the line x = 3.

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

A: Find the area enclosed by the x axis and the curve y= 4-x2

Q: Find the area between the curves x = y-1 and x =

A: Given:- x=y2 -1, x =2y2 -2 To find:- Area between given curves

Q: Find the area between the curve y = 6x – 2x and the x-axis between x 1, and x = 3. ||

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Q: Find the area between the x-axis and the curve y = -x² - 2x, -3 ≤x≤ 2.

A: Solution: Given that Curve is y = -x^2 -2x Area between the x axis and the given curve is

Q: Find the area bounded by the curve y = 62xe-62x and the x axis from x =0 to x = 4

A: Area bounded by the curve y=f(x) and x-axis from x=a to b is given as, ∫abf(x)dx Some common…

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

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Q: the area bounded by the curves y=2-x2 and y=x2 is

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

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Q: Find the area between the curve y (2.x + 3)2 and the x-axis, from x = -2 to x = 3.

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Q: Find the area between the curves. x = 0, x = 3, y = 2e3x, y = e3x + e6

A: To find the area between the curves, f(x)=2e3x and g(x)=e3x+e6, use the formula, A=∫ab[g(x)-f(x)]dx.…

Q: Find the area between the curve  y = x2 + 3x + 2  and the x-axis from  x = −1 to x = 1.

A: We have to find the area between the curve y=x2+3x+2 and the x-axis from x=-1 to x=1.

Q: Determine the area bounded by the curves y = -x² – 16x + 36 and y = (x – 2)².

A: Answer

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: 2. Find the area in the second quadrant bounded by the curve y = x' +4x² –x-4 and the x- axis.

A: To find: The area in the second quadrant bounded by the curve. Given: The equation of the curve is…

Q: 2. Find the Area bounded by the curve y=4-x2 and the x-axis.

A: 2. The area bounded by the curve y=4-x2 and the x-axis Note:    Multiple questions are given, we are…

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

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Q: Find the area bounded by the curve x=y²+2y and the line x=8.

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Q: Find the area included between x2+ y2= 4x and y2= x above x-axis

A: Find the area included between x2+ y2= 4x and y2= x above x-axis

Q: Find the area between the curve y = x² + 12x + 27 and the x-axis from x = -3 to x = -1.

A:

Q: Find the area between y = (x - 3) eX and the x-axis from x = 3 and x 9.

A: Give that

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 = x2 + 10x + 16 and the x-axis from x = −2 to x = 1.

A: We have limits of curve from x=-2 to x=1

Q: Find the area between the curves.  y = |9x|  ,  y= x^2 - 10

A: First we graph the functions. They cut at (-10,90) and (10,90)Area from x=-10 to x=0 is equal to the…

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

A: y = x4/3, y = 2x1/3

Q: Find the area between the curves x=y² –1 and x = 2y² – 2.

A:

Q: 2. Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

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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=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 in the second quadrant bounded by the curve y = x' +4x² – x – 4 and the x – axis.

A:

Q: How can I find the area between the curves?  x=y2-1, x=1-y2

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

A:

Q: Find the exact area below the curve y = x°(1 – x) and above the x-ax is. %3D

A: y=x31-x Diagrammatic representation of the required area is,

Q: Find the area of the region lying between the æ- In(9x) – 1 axis and the curve y = to the right x2…

A: Solving by area formula

Q: Find the area under the curve y = lines x = 1 and x = 5. 3x² + 4x + 1 bounded by the x-axis and the

A: Area under the curve y=3x2+4x+1 bounded by x-axis and x=1 to x=5.

Q: Find the area enclosed between the two curves y=4-x^2 and y=x^2-2x.

A:

Q: Find the area of the region between the curve y = 2x/(1 + x2) and the interval -2<= x <=2 of…

A: Find the area bounded by curves

Q: Find the area between the curves x2 and 6x – 5

A:

Q: Find the area between the curves y = 4x° and y= 3x + 1.

A: Given the curves y=4x2 and curve y=3x+1. We need to find the area between two curves.

Q: 1. Find the area between the curves x2-y 9 and the line y 2x-6 %3D

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Q: Find the area between the curves. y=x² - 23, y = 9 – 4x

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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 curves: y = x3 – 12x? + 20x and y = -a3 + 12x2 – 20x

A: Solution )

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.