While evaluating the area of the region bounded by two curves Vy = z and y- 11z + 24 = 0, the values of z of ntersecting points are O r = - 3,8 O r = - 3,-8 O x = 3,-8 O r = 3,8

Q: Find the area of the region bounded by the line y=x, x=2 and by the curve y= (1/x2)

A: Area of the region shaded below÷

Q: find the region bounded by x= Y-y3 ,X=1 = 1 Y=L, revolved about o X- axis

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Find the area of the region under the given curve from 1 to 2. 5 y = X° + 4x

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Q: 2. Find the cerntroid of the area bounded by the curve y= 2x + 1 x+y =7 and x= 8

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Q: Find the area of the region bounded by the curves: a) y=2x and y = 8 from x =-2 to x=2

A: You have posted multiple questions. As per the instruction, we will be answering only the first…

Q: Sketch the region enclosed by the curves x-6=3y and x-24=(y-6)^2 and compute the area.

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Q: Sketch the region bounded by the curves x = Vy + 3 , x =y+1 and evaluate the area

A: .

Q: Sketch the region bounded by the curves y = vx + 4 , y=x +2 and evaluate the area.

A: Given Curves are     y = x+4   and    y = x+2  first equation can also be written as  x = y2 -4 now…

Q: Find the area of the region bounded above by y = e x  , bounded belowby y =  x , and bounded on the…

A: Here the objective is to find the area of the region (A) that is bounded above by y = ex and bounded…

Q: Sketch and shade the region y = x² – 1, hence find the total area between the given curve and the…

A: The standard form of a parabolic function is where (h, k) is the vertex. This standard form is also…

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 of the region bounded by the given curves. (22) y = cos x + 1, y = x, x = 0, x = 1

A: First of all we need to draw graph of all functions and then find out the common region and finally…

Q: Determine the area of the region bounded by 3x - 5y + 4 = 0 and y-axis from y = 2 to y = 5.

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Q: Find the Area bounded by the given curves. y = 2x + 1 ,  y = 7 - x ,  x = 8

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Q: Sketch the region enclosed by the given curves andfind its area. y = x2 ,y = 4x - x2

A: Let us find the point of intersection by equating the two curves  x2=4x-x2 x2+x2-4x=0 2x2-4x=0…

Q: find the area of a region bounded by the curves y= x^3, y= x ln(x^2), x=1 and x=2

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Q: || 2. Find the area of the region enclosed by the curves x = 2y² – y + 1 and x y² + y + 4.

A: The area between two curves is given by: Where a and b are intersection points of the curves f and…

Q: Find the area of the region bounded by the given curves. c.)   y=4x-4x2, y=0, x=1, x=3     Ans.…

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Q: a. Find the area of the region bounded by the curve y = x³ and the line y = 4x. ovis for

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Q: While evaluating the area of the region bounded by two curves Vy = x and y – 14x + 48 = 0, the…

A: In this question we have to solve both equation by putting value of y from one to another equation.…

Q: Find the area of the given region y = tanh 2x

A: Given curve and figure: y = tanh 2x

Q: 1. Find the area of the region enclosed by the line x = 2y and the curve x = y - y?

A: We will find out the required area.

Q: Sketch the region bounded by the curves y = vx – 2 , y = x – 4 and evaluate the area

A: Solve by integration

Q: Find the area of the region bounded by the graphs of the equations y = e, z = 0, z= 5, y = 0

A: To find the region bounded by the following graphs of equations,  y = ex  x = 0 x = 5 y = 0

Q: Find the area of the region enclosed by the line x = 2y and the curve x = y3 - y?

A: To calculate the area of the region bounded by the curves x=fy and x=gy, use the formula…

Q: Find the area of the region under the curve y = 6x² + 4x + 5 from x = -1 to x = 2.

A: Solve the following

Q: = Find area of the region bounded by x² + y² = 4², 10y = -6x and 13y 8x where y > 0. Leave your…

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Q: Find the integral for the area of the region bounded by y = 2x+4, y = 2-3x, and y = -x using a…

A: Using vertical strip form double integral then integrate

Q: Sketch the region enclosed by the given curves and find its area. у — y = 1/x, у — х, у—x, х>0

A: The given curve is: y=1xy=xy=14xx>0  Sketch the region enclosed by the given curves and find its…

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 area of the region bounded by the given curves. y = x², y = 4x – x² - ly=x²

A: We have to find area of bounded region.

Q: Find the area of the region bounded by the 1 following y= 1 and x = 2. 2 -, y = X

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Q: 1/ Find the area of the region enclosed between the curves y= 2x+10 and y=4x+16 and ,x=-2 and x=-5?…

A: Area under curve

Q: y² = x y = x³

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Q: Find the area of the region bounded by the given curves: yx = 1, y= 0 , x = 1, x= 3

A: Given: Find the area of the region bounded by the given curves: `yx=1 y=0 x=1 x=3`

Q: Find the area of the region bounded by the given curves. y = 9x In(x), y = 36 In(x) %3D

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Q: Find the area bounded by The curves/lines 4y=x-2 Inx, y=0,x=1,x=4

A: Guven curves are 4y=x2-2lnx,y=0,x=1 and x=4

Q: 2. Find the area bounded between the curves: y = x², y = 4 – 3x, and x = 2 %3D

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Q: While evaluating the area of the region bounded by two curves y√=xy=x and y−15x+54=0y−15x+54=0, the…

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Q: Find the area of the region bounded above by y = x^2 + 1, bounded below by y = x, and bounded on the…

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Q: Find the area of the region bounded by the curves x = =Dy² +2, y y = x-4 and y = 0.

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Q: Find the area of the region bounded by the curves y= x2 x3−3x and y= 1 x3−3x on the interval…

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Q: 4) Sketch the region and find the area bounded by + = 1, y = ±3 and y = x + 4 using double…

A: We have to find the area of the region.

Q: Find the area of the region bounded by the given curves. y = 8 In(x), y = x In(x)

A: We first sketch the situation using a graphing calculator  y=8ln(x) (violet) y=xln(x) (black) x…

Q: Sketch the region enclosed by the given curves and decide whether to integrate with respect to x or…

A: This question can be solved using application of integrals to find area under curves.

Q: Find by double integration the area of the region in xy, plane bounded by the curves y = x2 and y =…

A: Using vertical strip

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

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Q: Find area of the region bounded by x2 + y2 = 6?, 5y = -7x and 2ly = %3D 11x where y > 0. Leave your…

A: The region bounded by x2+y2=62, 5y=-7x & 21y=11x where y ≥0

Q: While evaluating the area of the region bounded by two curves V/y = x and y – 10x + 21 = 0, the -…

A: We will find interesting points.

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.