'Find the area enclosed by the following points using: Simpson's Rule 2 4 8 14 18 21 f(x) -3 -1 4 6. 7 8 12

Q: Determine the area bounded by g(x) = x³ – 4x + 7 and h(x) = x + 5. %3D -

A: Given- g(x)=x3−4x+7 and h(x)=x+5 To Find- The area bounded by the above curves.  Concept Used-…

Q: Find the area bounded by the following curves.  x = 1/2, x = 1, y = 0, y = √ 1-x2/x

A: Given: The curves are

Q: What is the area of the region bounded between the graphs of x= y + 1 and r = 3- y? O 7/2 O none of…

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Q: Find the area of the region bounded above by y = -x² + 2 and below by y = x². 4 3 2 & A wit 543-2-11…

A: Given the curves y=-x2+2 and y=x2 . The objective is to find the area of the region bounded above by…

Q: ii, Find the area under the graph y=5x⁴between the limits x= 1 and x=3.

A:

Q: Let A denote the area enclosed by the equations y = x and y = 2 -x. Then A is S/212 7/29/2 3

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Q: 6. Find the area bounded by y= In x, y = 0 and x = e.

A: Area of a curve y=f(x) bounded by x=a, x=b is given by, A=∫abf(x)dx ln(e)=1, ln(1)=0

Q: The area bounded by the line y = x, the x - axis, the ordinates x =1, x = 2 is 3/2 O 5/2 O 1/2 7/2

A:

Q: Find the area enclosed by the following points using: Simpson's Rule 4 6. 8 11 14 17 20 f(x) -3 -1 4…

A: The Gaussian quadrature method is an approximate method of calculation of a certain integral…

Q: 1. Find the area of the region bounded by y = 4-x?, y = x + 2, x = -2, and x = 1.

A: As per our guidelines we ate allowed to answer one question at a time. Resubmit the other questions.

Q: Calculate the area between x=y+3 ,x=y^2 from y=-1 to y=1 7/3 18/7 32/6

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Q: The area bounded by the curve y = 3/x and the 9 above the x – axis lines x = 4 and x = is _square…

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Q: The area bounded by the line y=x, the x − axis, the ordinates x =1, x =2 is ___ O 3/2 sq units O 5/2…

A: area

Q: 4. Calculate the area of the bounded region = y' +3 y=3 -=1 y=-1 -1 4 5 6 7 9 10 11 12 A. 52/3 С.…

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

Q: Find the area between the graph of x = and the y-axis on the interval [1, 4]. 4 3 2- 1 0.5 05 1 1.5…

A:

Q: Compute the area bounded by the functions: 3y and x = y? - 10

A: From the given functions the bounded region is as shown below. Now find the point of intersection…

Q: 7. Find the area bounded by the curve y = x? +x + 4, the x-axis and the ordinates x = 1 and x = 3.

A: Given; y=x^2+x+4

Q: Use the Right Rectangular Approximation Method with n=2 to approximate the area under the curve of f…

A: Given function :   Integration of function gives area under the curve.

Q: x? + y? = 4 and x? + y? = 4x Compute the area bounded by

A: The given equations  are

Q: Find the area bounded by the curve of y = x' + 3 and the x-axis from x = -3 to x = 1 Approximate are…

A:

Q: An area bounded byy = 0, x = 0, and y = e*, is revolved about the x-axis. 7. CD method is…

A: Yes it is true we can use CD method here for area revolution and find volume generated due to area…

Q: y = x², y = 0, x = 1, and x = √5

A:

Q: 3. Find the area of the region bounded above by y=e*, bounded below by y = x, and bounded on the…

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Q: What is the area bounded by the curve y2 = 4x and x2 = 4y? А. 5.33 В. 6.67 С. 7.33 5- -5 5 D 8 67

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Q: 3 8) Find the area bounded by y = x = 0, y = 0, and x = 2. Vs1 - 9x2

A: Given function  y=381-9x2 y=39(9-x2)y=339-x2y=19-x2 To find area bounded by the curve

Q: Find the area bounded by r = 6cos (30).

A: Given: r=6cos3θ

Q: Use Simpson's Rule and all the data in the following table to estimate the value of the integral 21…

A: Simpson’ rule:

Q: 1. Find the area of the region bounded by f(x) = x, the x-axis, and the vertical lines x = 0 and x…

A: Given: 1.f(x)=x3  x=0 and x=1

Q: 7. The area bounded by y = , y = -x² ,x = 1 and x = 2 equals 14 А. 17 В. 6. 19 С. 3 D. 6

A:

Q: Find the area bounded by the following curves and lines. y=(x^2+1)/(x+1) and x+3y=7

A: Given  Region is bounded by the curve y=x2+1x+1      and  x+3y = 7 now  find the  intersection point…

Q: В. Find the area enclosed by the given curve, the x-axis, and given lines. x²+10, x=1 and x 3 3 4. y…

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

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Q: 1. Find the area of the region bounded by y = x? + 4, y = x, x = 0, and X = 3.

A: Note : As per authoring guidelines, when multiple questions are posted, then only first question or…

Q: 14. Determine the area bounded by x = 1, x = 2, and y = e*.

A: To solve this problem, the function y needs to be integrated from x=1 to x=2

Q: Find the approximate area under the function f(x)=2.5-2sin(πx/6) using the four middlescribed…

A: From the given picture we see that the middle points are x=1,3,5,7 So we find the x values at these…

Q: Find the net signed area of ƒ (x) = x - 2 over the interval [0, 6], illustrated in the following…

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Q: 3. xy = a², y = 0, x = a, x = 2a.

A:

Q: 7. Find the area bounded by the curve y = x e¯** , the x-axis and the maximum ordinate.

A:

Q: x? +y? = 4 and x² + y? = 4x 1) Compute the area bounded by

A: Given

Q: (b) A Curve is drawn to pass through the following points: t 1 1.5 2 2.5 2 2.4 2.7 2.8 Find the area…

A: Simpsons 3/8 rule is used to approximate definite integrals. The integral can be approximated to…

Q: 7. What is the area bounded by the curve y=x and the line x-4=0? A. 10 32 B. 3 C. 32 D. 11

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Q: Find the area of the region a. f(x) = 2e*/2 y 4 1 2 4 3. 5. 3. 2. 1.

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Q: Determine the area bounded by g(x) = x³ – 4x + 7 and h(x) = x + 5. %3D

A: Two functions are given

Q: В. Find the area enclosed by the given curve, the x-axis, and given lines. 1 -x+10, x=1 and x=3 3 4.…

A: Using area formula,

Q: The shaded region has what area? 1.5· y = x 1 0.5 -0.5 0.5 1.5 2 2.5 3 3.5 4 4.5 1 (x – 3) -0.5 Y :…

A: We want to find the area of the shaded region. The shaded region is a triangle, so to find the area…

Q: The area bounded by the curve y = 3/x and the lines x 3 and x = 8 above the x axis is _square units…

A: All options are incorrect.

Q: 1) The region R in the first quadrant is bounded from above by y = 2x+9 and below by y = x² +3. Find…

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Q: х — 18 Find the area bounded by Y x = 5, x = 6, and y = 0. г? — 5а — 24 -

A: To determine the area bounded by the given curve.

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.