Sketch the curve, y=-x +9. Then, find the area between the curve and the x- - axis over the interval, -3

Q: Find the area bounded by the curve y = x exp(-x²), the x-axis and the vertical line passing through…

A: Given: The given curve is, The x-axis and the vertical line passing through the maximum coordinate.…

Q: Find the area of the region between the curve y 4 In x and the horizontal axis for

A: We have to find the area of the region between the curve  y=4 ln x and the horizontal axis for…

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

A: See below

Q: What is the area of the region enclosed by the curve y=x(x-1) (x-2) and the x-axis?

A: Given:            Curve: y=xx-1x-2             Area =∫01xx-1x-2 dx+-1∫12xx-1x-2 dx…

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 curves. x = -3, x = 0, y = 1 -x2, y = 0

A:

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 between the curves. x = 1, x = 2, y = 3x3 + 2, y = 0

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Q: Find the area bounded by the curve y=4x-x? and the lines x=-2 and y=4.

A: The given equation forms a downward parabola.

Q: Find the area of the curve bounded by the curves y=x* and y=3x+4.

A: We have to find th: e area of the curve bounded by the curves y=x4 and y=3x2+4.…

Q: Find the area bounded by the curve: y = 8x – x² and y = 3x

A: a) Consider

Q: Find the area of the region in the first quadrant bounded by the line y=3​x, the line x=4​, the…

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Q: Find the area between the curves. x = -2, x = 1, y = 2x, y = x2 - 3

A: Given curves,  y = 2x y = x2 - 3 x = -2 x = 1 To find the area enclosed.

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

A: In this question we have to find Area.

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

A:

Q: Find the area bounded by the curve y (x- 2)(x + 1)(2x – 1) and x-axis.

A: We use integration to find the area.

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 curve y = x – and y = -x + 10x2 – 24x 10x + 24x

A:

Q: Find the area bounded by the curve f(x) = -x² + 10 and the x-axis. Give your answer correct to two…

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

A:

Q: Approximate the area under the curve y=f(x)=1/x  on the interval [1,4] , Using 3 rectangles

A:

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. x = -5, x=2, y = 3x, y = x² - 4

A:

Q: What is the area bounded by the curve y^2 = x and the line x - 4 = 0?

A: We have to determine area of bounded

Q: Find the area of the region bounded on the left by the curves y = e3x and y=3-x, and on the right by…

A: The area is the amount of space occupied by the surface. It is measured in terms of unit squares it…

Q: find the area of the region bounded by the curve y^2=x+1 , both by the x and y axes and the line x=8

A: Using Reimann sums, the area of the region R is given by Sn=∑k=1n∆Ak. This is simply the sum of…

Q: estimate the area under the curve y=x^1/2, from x=1 to x=3 using right end point estimate

A: SolutionGiventhe curve y=x,from x=1tox=3 we need to estimate the area  under the curve y=x1/2,from…

Q: area bounded by the curves y2= 6x and x2 = 6y?

A: Given curvesy2=6x or y=6xand6y=x2 or y=x26

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

A:

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

A:

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 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 Enclosed by the Curve x=7²-2t,y-VE and the Y-pris

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Q: Find the area of the region enclosed between the curves y= 4 -x^2 and x=3 and x-axis within the…

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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 between the curves y = x and y = -x

A:

Q: Find the area between the curve and the x-axis over the indicated interval. y = 25 - x2; [-5, 5|

A:

Q: : Determine the area enclosed between the curves y = x² + 1 and y = 7 - x

A: Area between two curves y=f(x) and y=g(x) between x=a and x=b is A=∫abf(x)-g(x)dx

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

A:

Q: Find the area bounded by the curve f(x) = -x² + 7 and the x-axis. Give your answer correct to two…

A: We have to find Area bounded by the given curve and x-axis.

Q: What is the area bounded by the curve y = x3, the x-axis, and lines x= - 2 and x = 1?

A:

Q: Find the area between the curves x=y^2/2 and y=x-4

A: First we draw the curves using graphing calculator.

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

A:

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: What is the area bounded by the curve y^2=x and the line x-4=0?

A:

Q: Find the area bounded by the curves y=ex+2, y-axis, y=1, and the line x=3

A: Find the area bounded by the curves y=ex+2 and y-axis, i.e., x=0, y=1, and the line x=3. Limit for x…

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

A:

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 between the curve y =53-* and the interval [0,2] on the x-axis.

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.