Find the area of the region under the graph of the function fon the interval (1, 3]. Flx) = Sx3 square units

Q: Find the area of the region bounded by the graph of the function f (x) = x, the X−axis, and the…

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Q: 1. Find the area of the shaded region. 3 y = Vx X 4 y = -x а.

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: 21) Find the area of the region in the first quadrant bounded by the line y = 8x, the line x = 1,…

A: We first sketch the region using a graphing calculator.

Q: Find the area of the region bounded by the curves.  y = x(x2 - 1) and the x-axis

A: Given curves are, y=x(x2-1)and the x-axis y=0 .   First, find the intersection points:…

Q: Find the area of the region in the first quadrant bounded by the curve y = √x² + 5, the x-axis and…

A: Given: y=x2+5 Graph of the functions given are

Q: Find the area of the region in the first quadrant bounded by the curve y = √√x² + 5, the x-axis and…

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Q: : Find the area of the region in the first quadrant that is bounded above by y x and below by the…

A: SOLUTION-

Q: 4.) Find the area of the region bounded by the curves y =x- 6x? + 8x and y =x - 2x

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Q: Find the area of the region under the graph of the function fon the interval [0, 61. f(x) = 6x- x2…

A: We will find the area of the region under the graph of the function f(x)=6x-x2 on the interval [0,6]

Q: Find the area of the region bounded by y = ex and y = 12 − ex and the y-axis.

A: Given, y=exy=12-ex and the y-axis   Find the area bounded by the region:

Q: Find the area of the region in the first quadrant that is bounded above by y = √x and below by the…

A: Now the diagrammatic representation of the area is,

Q: Find the area of the region bounded by the X – axis, the lines x = 4 and x = 6 and the curve X – 1 A…

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Q: Find the area bounded by the curve y = 8 – x and both coordinate axes in the first quadrant. Area of…

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Q: Find the area of the region above the curve y = x^2 - 6, below y = x, and above y = − x.

A: Given region bounded above by  y=x2-6  and y=-x  and bounded below by y=x

Q: Find the area of the region bounded by the curve y = xe* and the x-axis from x = 0 to x =3 1 0.5 y =…

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Q: Find the area bounded by the given curves. y = 3x2 and y = 27

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Q: Find the area of the region bounded by the curve y=1-–x2 and the x-axis. O 6 square units O 4 square…

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Q: D Find the area of region bounded by the Curve y= Xe and X-axis From X=otox=4 %3D

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Q: Find the area of the region between the curves y=x^3, y=-x, and y=1

A: Area=14 sq.units

Q: find the area of the region enclosed by the graphs of the functions. x = 4y, x = 24 − 8y, y = 0

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Q: Find the area of the region bounded by the curve y=1- x? and the x-axis. 9. 8 square units 6 square…

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Q: Find the Area of the region bounded by the graphs of the following functions 4x+y^2=12, y=x

A: Solve the equations to get the points of the intersections.

Q: Find the area enclosed by the given curves. 20) y = 2x - x2, y = 2x - 4 %3D

A: We first sketch the region using a graphing calculator

Q: f(x) = (e* – x); [0, 2]

A:

Q: Find the area of the region under the graph of the function f on the interval [a, b]. f(x)=ex-3;…

A: Area under curve

Q: Find the area of the region in the first quadrant bounded by the curve y = √x² +5, the x-axis and…

A:

Q: find the area of the region enclosed by the graphs of the functions. y = x3 − 2x2 + x, y = x2 − x

A: To find the area of the region enclosed by the graphs of below functions.

Q: Find the area of the region bounded above by y = −x² + 5 and below by y = 1.

A: Given, y=-x2+5 and y=1

Q: find the area of the region enclosed by the graphs of the functions. y = 4 − x2, y = 3x, y = 4

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Q: Find the area of the region bounded by y = x³ - 8 the x-axis and the y axis. 1/3 3 1/9 9

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Q: Find the area of the region under the curve y = f(x) over the indicated interval. f(x) = x 2 6 %3D…

A: In the question it is asked to find area under function f(x) with interval [6,∞).

Q: 3/ find the area for the region in the first quadrant bounded by the curve (y = 4x - x²) and line (y…

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Q: 4.Find the area of the region bounded by the curves y = x² – 2x and y = x.

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Q: Find the area of the region bounded by y = 13 / (49 − x2) and y = 1.

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Q: Find the area of the region bounded by the graph of the function f and the lines y = 0, x = -3, and…

A: Given:        f(x)=x2−2x

Q: Find the area of the region bounded by the graphs of y = 2e−x , y = 0, x = 0, and x = 2.

A: Given equations: y=2e-xy=0x=0x=2 The region bounded by the graphs of these equations is shown below:…

Q: Find the area under the curve y = xe for x > 1. area %3D

A: Given curve is y=xe-x for x≥1 Apply the area formula  ∫01xe-x dx      ⇒∫01xe-x dx⇒(-x-1)e-x01⇒1-2e-1…

Q: Find the area of the enclosed region bounded by the graphs of y=e^x, y=x, the y-axis and the line…

A: Here we have to find the area of the enclosed region bounded by the graphs of y=ex,y=x,the y-axis…

Q: Find the area of the region bounded by the functions s(x) = 6x and t(x) = 6x. %3D

A: Using basic integration...I have solved your question in detail ...hope you will get it…

Q: Find the area of the region bounded by the given functions. y = x2 , y = -x2 + 4x, x = 0, x = 2

A: To find the area of shaded region in the graph

Q: Find the area bounded by the indicated curves. y 2x, y 4-2x, x = 0 (x20) The area is

A: Given; y=2x^2, y=4-2x , x>0

Q: Find the area of the region bounded by the curves y = e", y = e¯, x = -2, and x = 1.

A: y=ex, y=e-x, x=-2 and x=1. The graph is,

Q: Evaluate the area of the region bounded by the graphs of the following functions. y = e0.25¤ , y =…

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Q: Find the area bounded by the given curves. y = 3x2 and y = 27

A: The given curves are y = 3x2 and y = 27.

Q: 3. Find the area of the region bounded by the curves y = x² and y = x/x+2. .

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Q: Q1: Find the area of the region bounded by y= Vx, y v4-x and x-axis.

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Q: Find the area of the region in the first quadrant bounded by the curve y = √x² + 5, the x-axis and…

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Q: Find the area A of the region bounded by the line y = x and y = 6 – x²

A: Area between curves

Q: f(x) = e-=/2; [-1,2]

A:

Q: Find the area of the region between the curves y=|x| and y=x^2-2

A: Proceed as shown...

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.