Find the area between the curve y = -x< + 6x – 8 and the x-axis from x = 2 to x = 4. (Give an exact answer. Do not round.)

Q: Find the area between the curve y = x² + 8x + 12 and the x-axis from x = -2 to x = 0. (Give an exact…

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Q: Find the area of the region bounded by the curve y=1- and the x- axis.

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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 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 curve x = 2r*, y = 31 +1 and the x-axis, 0<t<2 !!

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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 a^2y = x^3, the x-axis and the line x = 2a

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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 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 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 bounded by the given curves. y = 3x2 and y = 27

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Q: Find the area between the curves.

A: Given: The curves are y =x and y =xx  .

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: Q- Find the area of the region bounded from the right by the curve x = 4 - y? ,from the left by the…

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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 under the curve y = 5xe- for x > 4. area =|| %3D

A: Explanation of the solution is 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: Find the area bounded by the curve y= lnx, the x– axis, the line x = e². A =1+e?

A: Use area formula

Q: Find the area bounded by the curve 5y2 = 16x and the curve y2 = 8x − 24 and provide a correct and…

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Q: Find the area of the infinite region in the first quadrant between the curve y = eX and the x-axis.

A: Given curve, y=e-xand x-axis Formula for the area of the region under a curve is given by A=∫aby dx

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

A: We have to find the area between the curve y=x3-6x2+8x and the x-axis.

Q: Find the area enclosed by the given curves. y = 2x - x2, y = 2x - 4

A: NOTE: Refresh your page if you can't see any equations. . given functions are

Q: Find c such that the area between the curves y z2 - c and y c -x is equal to 69. Round your answer…

A: Given that y = x2 - c2 and y = c2 - x2  and area of this 69  We find value of c . Here i attached…

Q: Find the area between the curves y = x²(x – 3) and y² + 8y – 16x + 48 = 0 -

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Q: Find the area of the region in the first quadrant bounded by the line y = x, the line x = 2, the…

A: the area of the region in the first quadrant bounded by the line y = x, the line x = 2, the curve y…

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 bounded by the curve 5y^2 = 16x and the curve y = 8x – 24.

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Q: 2. Find the area enclosed between the curves y =x² +2x +11 and y =-4x+2.

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

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Q: Find the area enclosed by the given curves. y = 2x-x2,y 2x-4 31

A: Explanation of the answer is as follows

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

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Q: Find the area enclosed between the x-axis and the curve y = (x+ 3)²,0 < x < 1.

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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 between the two curves y=4-x^2 and y=x^2-2x.

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

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Q: Find the area bounded by the given curves. y = 8x' + 3 and y = 8x + 3 square units

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Q: Find the area of the region between the curves ソ=x and y=x? for 0<x<1

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

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Q: Find the area enclosed between the line y 1 and the curve y = x2 – 4x + 4.

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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: 4. Find the area enclosed by the curve: x=t2 – 2t, y= vt and the y-axis

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

A: To find the area between the curve y=x2+10x+16 and the x-axis from x=-2 to x=1. This is given by…

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.