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

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 under the curve 4x²-3x+6 between x = -2 and x=3

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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 between the curves x² and 3x – 2

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

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

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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 y = ln x and y = ln 2x from x = 1 to x = 5.

A: The given two curves are,

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

A: In this question we have to find Area.

Q: Estimate the area under the curve f(x) = 2x from 0 to 1 using R4. Leave your final answer as exact…

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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: Find the area under the curve y =3x2-2x from x= 1 to x =5.

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Q: Solve for the area beneath the curve y = -(x – 1)² + 10 and above the axis from x = -1 and x = 2.

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Q: Find the area between the curves: y = x³ – 10x? + 16x - x³ + 10x² – 16x 3 and y = -x° + 10x?

A: Consider the figure given below :

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: 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 total area between the curve g(x)=x^3 + 2x^2 -x-2 and the x-axis, from x=0 to x=2

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Q: Find the area between x-axis and the curve defined by   y=2·x2−6·x on the interval [0‍,4].

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Q: Find the area between the curve f(x)=x^3−110 and the​ x-axis from x=1 to x=3.

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

A:

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

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

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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 curve ​f(x)=x^2​+15 and the​ x-axis from x=3 to x=5.

A: Given query is to find the area under the curve.

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 x=63-7y^2 and x=7y^2-63

A: Here two curves are given and we need to find the area between them. The curve equations are shown…

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

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Q: Find the area of the region between the curve y = 21-x and the interval -1≤ x ≤ 1 of the x-axis.

A: Given: y=21-x, -1,1

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 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: 8) Find the area between the curves: y = x'-9x + 14x and y =-x +9x2 - 14x

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Q: Find the area between the curve y = tan x and the x-axis from x = -π/4 to x = π/3

A: y=tanx from x=-π4 to x=π3. The graph is,

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 curve and the x axis over the indicated interval. Y=4-x square; [-2,2|

A: Given: Y=4-x2 to find out: area between the curve and the x -axis over the interval [-2,2]

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: The area under the curve y =3/x over the interval [1.4]is equal to: 14

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Q: Find the area bounded by the curve y=10+4x+x^2 and x-axis from x=-3 to x=-1.

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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.