Determine the area bounded by y = 4ax, y=2a and x=0 for a = 3 %3D

Q: The area bounded by y = e*, y = 2, and the y– axis is equal to

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Q: Find the area bounded by y = x3, y = 0, and x - 2 = 0 at the x axis and y axis.

A: The given curves are,

Q: Find the area bounded by y х — 17 2, x = 5, and y = 0 . 36 (Round the answer to four decimal…

A: Answer

Q: 4y = x 2 – 2lnx, y = 0, x = 1, x = 4.

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Q: Find the area included between x + y* = 4x and y = = x above x-axis.

A: Consider fx and gx be two functions between a,b and fx≥gx .Then area between graph of these two…

Q: Find the area bounded by y = (1 ²)² and y = 0.

A: y=(1-x2)2 and y=0

Q: Find the area enclosed between y = x and x = 2 − y 2

A: Given, y=x and x=2-y2 We have y=x and x=2-y2⇒y=2-y2⇒y2+y-2=0 By solving the above equation, we get,…

Q: Find the area enclosed by x – y = 0 and 5x – y = 4

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Q: Find the area between y = x^2 + 4, x = 1 and y = 0.

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Q: Find the total area of the region between the curve and the x-axis. 2) y = (x + 1/x; 4 sx s 9

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Q: Find the area bounded by y = 2; y = √x + 2; and y = 2 - x. Show your solution below.

A: We are given :  y=2  y=x+2 y=2-x First of all we will plot the graph for these 3 curves.

Q: Determine the area of the region bounded by y = xvx? + 1,y = e¯i,x = -3 and the y-axis.

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Q: Determine the area of the region bounded by y = xvx2 + 1, y = 1 e 2x, x = -3 and the y-axis. %D

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Q: A// Find the area of the region bounded above by (y= e), bounded below by (y x)and the boundary line…

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Q: Find the area between x = y2, x - axis, x =y +2 To find the intersect points

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Q: Find the area bounded by y = (11 – x)7, the lines 3x=2, x=10, and the x-axis

A: We have to find the area bounded by the curves.

Q: Find the area bounded by the ff. curve and line: y = xe^– x , the x-axis and the maximum ordinate

A: The curve y=xe-x, we have to find the area bounded by the curve, the x-axis and the maximum…

Q: Find the area between y=x+3 and y=x^2+1

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Q: Find the area bounded by the given curves. y = 8x3 + 7 and y = 8x + 7 _________ square units

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Q: Find the area bounded by y=(1-x^2)^2 and y=0   Solve by drawing a figure to show the bounded…

A: From the given curve the bounded region is shown below:     Now using the double integral method to…

Q: Determine the area bounded by the graphs of the following equations. y=coshx  , y=3

A: Given that, y = coshx  and   y = 3 we have to calculate the area bounded by both equation, Solve…

Q: Find the area bounded by the curve y=x^2 and the x-axis and the lines x=1 and x=3.

A: Given: y=x2, x=1, x=3, and x-axis or y=0. So, from the given curves the bounded region is as shown…

Q: Find the area bounded by the curves x 2 = y − 1 and = y − 3 .

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Q: The area formed by the boundaries y=1, x=2, and y=e^(-x) is closest to:

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Q: Find the area bounded by y² = 4a(y-x), y² = 2a(x+2y-3a) and the x-axis

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Q: Find the area bounded by y^2=4a(y-x), y^2=2a(x+2y-3a) and the x-axis.

A: Given: y2=4a(y-x), y2=2a(x+2y-3a)

Q: find the area enclosed by the graphs in two ways: by integrating along the x-axis and by integrating…

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Q: Find the area bounded by y = 2x2 - 4 and y = 5. Leave your answer correct to 2 decimal places.…

A: This is area under the curve problem

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

A: To find the area bounded by the curves y2=8x and y=2x Solution :  Let y2=8x    ⋯(1) Since y=2x, we…

Q: Solve the area bounded by the curve x=y^2 and the line y=x+1, y=2, and y=-2. Graph manually.

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Q: Find the area bounded by y=2*, y = 2x2, the y - axis and x = 1 Write your final answer in two…

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Q: Find the area bounded by y2 = 4x and y = 2x – 4.

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Q: Find the area bounded by the given curves. y = x2 − 5 and y = 4 − 8x2 _____________ square units

A: Given curves y=x2-5 and y=4-8x2. The objective is to find the area bounded by the curves.

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 bounded by y^2 = 4a (y-x), y^2 = 2a (x+2y-3a) and the x-axis

A: We can use double integral to solve it.

Q: Sketch the graph and find the area bounded by the curves for y = 2x² and y = x² + 4

A: Given query is to find the area bounded by the curves.

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

A: Graph of the function y=x(x-1)(x+1) will be as following

Q: . Find the area bounded by y = (11 – x), the lines 3x=2, x=10, and the x-axis.

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Q: Find the area of the region bounded by the curve y = ln x, the x axis, and the line x = e^2

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Q: Find the area bounded by y=2%, y = 2x2, the y - axis and x = 1 Write your final answer in two…

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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 bounded by the parabola y2= 4x, the x – axis and the lines x=1 and x=3.

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Q: Determine the area bounded by the parabola y = x^2, the line y = 6-x, and the x-axis

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Q: Find the area bounded by the curve and y+ 4 = 0 y=x²-3x 3X

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Q: Find the area bounded by the line y = x+2 and parabola y = x².

A: We can solve this as follows:

Q: Find the area bounded by y = x³ – 3x and y = -4.

A: To find the area bouded by the curves.

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: Find the area bounded by the curve y = 4x - x² and y = 3. Answer:

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

A: The area under a curve is the area between a curve fx and the x-axis on an interval a, b given…

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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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.