Sketch the region bounded by the curve 4xe¯", the x-axis, and x = 3, and find the area of the region. Round your answer to four decimal places.

Q: 9: Find the area of the region enclosed by the curves y x? and x = y about x-axis

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Q: Sketch the region bounded by the curve 8xe Round your answer to four decimal places. the x-axis, and…

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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: Sketch the region bounded above by the curve 6xe−x6xe-x, the x-axis, and x = 3, and find the area of…

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Q: Find the exact area of the region that lies under the curve given by y = 10/2x +1, 0<x <1 %3D

A: We know the area of the region that lies under the curve  y=f(x),  a≤x≤b is given by Area =∫aby dx…

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

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Q: Fin the area of the region that lies between the curves

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Q: Find the area of the region in the first quadrant bounded on the left by the​ y-axis, below by the…

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Q: Find the area of the region bounded by the curves y= 2² - 3 and y = 2x + 5.

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Q: Find the area of the region bounded by the curve y=x^2−1 and the line y=15.

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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 of the region between the curve y = 4 3-x and the interval 0 sxs2 on the x-axis. 60 In…

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Q: Find the area of the region cut from the first quadrant by the curve x1/2 + y1/2 = a1/2.

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Q: Sketch the region whose area is given by the definite integral. 8. x dx

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Q: Find the area of the region between the curves (x = y² ) and (x = y + 2 ) in the first quadrant.

A: The formula to find the area under the region between the curves is Area=∫y=ay=b[f1(y)-f2(y)]dy.…

Q: Find the area of the region that is enclosed between the curves y = x² and y = x + 6.

A: The given curves are, y=x2 and y=x+6. The objective is to find the area of the region that is…

Q: Find the area of the region bounded by y = 3x + 10, y = -4x + 1 and x = 12. Leave your answer…

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Q: Find the exact area of the region that lies beneath the curve y = 8 sec2 (x), 0<x < n/3.

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Q: 2. Find the area of the region enclosed by the curve =x- 4 and y = x - 2.

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Q: Find the area of the region between the line y = −x and the curve y = x2 + x − 3

A: Area of the region is 32/3

Q: Find the area of the region bounded by the curve y = 9 - x2 and the x-axis. Answer:

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Q: Find the area of the region bounded by y = 4x + 9, y = -6x + 9 and x = 14. Leave your answer correct…

A: Area of region bounded by given curves are evaluated.

Q: Sketch the region bounded above by the curve 7e sin(Tx), the x-axis, and r = 1, and find the area of…

A: The graph of the above function is :

Q: Find the area of the region enclosed by the line y=4x and the curve y= x+ 3x.

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Q: What is the area of the region enclosed by the curve y=e^x and the lines x=-1 and y=3?

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Q: Find the total area of the region between the curve and the x-axis. 9) y = (x + 4)3; 0 <x<3

A: The Area Under a curve The area under the curve between two points can be found by a definite…

Q: Sketch the region bounded above by the curve 7e- sin(Tx), the x-axis, and x = 1, and find the area…

A: Given,

Q: Sketch and find the area of the region below the interval [-6,-5] and above the curve y 器.

A: Given, Find area above y=x325 and below [-6,5]

Q: Find the total area of the region between the curve and the x-axis. 7) y = 2x - x2; 0 sx<2

A: Given, The curve  y = 2x-x2   ;  0≤x≤2 We have to find the area of region between the curve and the…

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

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Q: Graph the region between the curves. And Compute the area of the region. (Round your answer to five…

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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: Graph the region between the curves and use your calculatorto compute the area correct to five…

A: The equations given are , y=21+x4 , y=x2. The region bounded by these curves is shown by the…

Q: 5) Calculate the area of the region between the curves: y=2-x² and y=x²

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Q: Sketch the region bounded by the curve 8xe¯ª, the x-axis, and x = 2, and find the area of the…

A: To sketch and find the area of the region.

Q: Find area of the region under the curve y=8−3x^2 and above the x-axis

A: First we find where y=8−3x2 cuts x axis. We set y=0 and solve for x

Q: Find the area of the region between the curves 4x + y = 12 and x = y. Area between curves =

A: R

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

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Q: 5) Calculate the area of the region between the curves: y = 2 = x² and y = x²

A: We can find the area as below.

Q: 7) Find the area of the region enclusced by the curves y=x² and

A: Please refer the attached image for complete solution. THANK YOU !

Q: Find the area of the region bounded by the curves y = 6 – x² and y = x + 4.

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Q: Find the area of the region bounded by the curves y = 6 – x² and y = x+ 4.

A: intersection  6-x2=x+4x2+x-2=0x2+2x-x-2=0x(x+2)-1(x+2)=0(x+2)(x-1)=0x+2=0 or x-1=0x=-2 or x=1⇒-2≤x≤1

Q: Sketch the region bounded by the curve 3xe¯", the x-axis, and x = 4, and find the area of the…

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Q: Sketch the region below the curve y = x – x² and above the x-axis and find its area.

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Q: Find the area of the region bounded by y = 7x + 7, y = -9x + 4 and x = 15. Leave your answer correct…

A: The solution of the problem is given in the next steps.

Q: Find the area R- region in the first quadrant that lies below the curve y=x^2+4 and is bounded by…

A: The given problem is to find the area of region R bounded below by the given curve and the line.…

Q: 2 x = 8 – y, x=y¯ - 8 ?, x =y² - 8

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Q: Find the area of the region bounded by y = 4x + 6, y = -3x +1 and x = 15. Leave your answer correct…

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Q: Find the area of the region in the first quadrant bounded by the line y = 8x, the line x = 1, the…

A: Intersection Points are:  The line x=1 will intersect the x-axis at (1,0) because y is 0 at…

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.