Each of the regions A, B, and C bounded by the graph of f and the x-axis has area 3. Find the value of + 2x + 3] dx. В A -2 C 2

Q: ii) area bounded by x = 1, y = 1, x = 3, y = 3, and x +y = 5 equal to 25n а. 44 49n b. 44 367 с. 44…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Below is the graph of y= r +5. 20] 15 10 -2 -1 0 1 4 The area bounded by y= z+5 and the zaxis from…

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Q: 11. Find the area of the region bounded byy = (x - 1)² + 1, the x -axis, x = -1, and x = 2. A. -6 C.…

A: Here we are using integration method to find the area of the given region.

Q: 4. Find the area of the region bounded by the graphs of f (x) = x³ +x2 – 6x and g(x) = 2x – x2 20 А.…

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Q: Find the area of the region bounded by the graph ofy =1/x the x-axis, and the vertical lines x = 1…

A: The area is calculated by taking a rectangular element of width  dx and height y. The total area is…

Q: 10.Which of the expressions below could be used to correctly compute the area bounded by the graph y…

A: Given curves y1=10x-4x2 & y2=2x

Q: Which of the following gives the area of the region between the graphs of y = |x| and y = 5

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Q: Let b 1 be an integer. The area of the region bounded by the graphs of the functions y = 20bx and y…

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Q: 4 The net signed area in the above graph can be written as (mæ + b)dx, where c = d and b = = U

A: The net signed area in the above graph can be written as ∫cdmx+b dx, where c=?,  d=?m=?, and b=?

Q: Find the areas. of. the region k bounded by.the graphs of the given equations R .y=0,X=2. and. x=…

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Q: 1 Find the area of the region between y =x and y =x for x in [-1, 1]. O a. 1 O b. 1 1 Oc. 14 d. 1 10…

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Q: Each of the regions A, B, and C bounded by the graph of f and the x-axis has area 3. y В -4 A 2 C…

A: So here we are going to use integral formula and seperates into two part and calculate them and…

Q: 28. Find the area, if it is finite, of the region under the graph of y = 1/V(3x – 2)³ over [6, *).

A: area =∫6∞ydx

Q: Each of the regions A, B, and C bounded by the graph of f and the x-axis has area 3. Find the value…

A:

Q: Each of the regions A, B, and C bounded by the graph of f and the x-axis has area 3. Find the value…

A: To find the integral of the given function Given : A = B = C = 3  Area below the x- axis will be…

Q: The area of the region bounded by y-19-x, the x-axis and the line y-x in the first quadrant is: O…

A: Given: y=9-x2 y=0 y=x Calculation: Use an online graphing calculatora and obtaine the bounded region…

Q: 1. Find the area of the given region bounded by the graphs of y, = x² + 2, y2 = 4 – x², and y3 = 2 –…

A: The area of the region enclosed by curves A=∫abfx-gxdx. Obtain the intersection points of y1,y3 as…

Q: The area bounded by the curve y = 3x and the lines x = 4 and x = 6 above the x - axis is O 30.00…

A: Given that y=3x at x=4 and x=6  find out area bounded by the curve

Q: Each of the regions A, B, and C bounded by the graph of f and the x-axis has area 3. Find the value…

A: To determine the value of integral

Q: Below is the graph of y = x² +5. 141 12- 10 -2 -1 8- 6- 4- 2 0 1 2 3 The area bounded by y = x² +5…

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Q: 4. Find the area to the right of z= -1.8

A: We need to use the concept of Standard normal distributions

Q: Find the area of the region enclosed by the given graphs. a)f(x) =x^2+x-9 and g(x) = 3x-1 b)-x^2+…

A: Let us take two curves f(x) & g(x), then area of region enclosed between these curves is given…

Q: 3. Find the area bounded by the graph of the indicated equations over the given intervals (when…

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Q: Let b, c, andd be positive numbers, and let f(x) = cx + d.The region R bounded by the graph of f.…

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Q: 5. Each of the regions A, B, and C bounded by the graph of f and the x-axis has area 3. Find the…

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Q: Draw the graphs and find the between the area curves f(x) = (-1)*x² +(-1)°(c+3)x+(-1)*(a+2) and…

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Q: The total area bounded by the graph of y 2 -1 and the x-axis is represented by Select one: O…

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Q: 3. Find the area of the region bounded by the graphs of y = 2 - x² and y = -x. 4.5 O 1.5 O -1.833…

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Q: A region bounded by f(x) = x² + 1, y = 1, and x = 2 is shown below.

A:

Q: Each of the regions A, B, and C bounded by the graph of f and the x-axis has area 3. y В A 2 C Find…

A: The graph of f(x) has area 3∫-42f(x)+2x+1dx

Q: Draw the region whose area is given by the definite integral. Ay 40- Sa2-2 36 - 2x)dx 32- Use the…

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Q: *** Which of the following represents the area of the region bounded by y= x+2 and y= x2 ?

A: Area is bouded by curve y=x+2  and y=x2

Q: The area, under the graph of y=x^2 from x= 0 to x= 1, is: y=r² O 1/3 O-1/3 O o *

A:

Q: Each of the regions A, B, and C enclosed by the graph of f and the x-axis has area 6. Find the value…

A: Answer and explanation is given below...

Q: The area of the region between the graphs of y = x² and y = -x from x = -1 to x = 0 is O is Li (2² +…

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Q: Estimate the value of k (0 < k < 1) so that the region enclosed by y = 1/√1−x2, y = x, x = 0,…

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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: (1) Find the area enclosed by the two functions f(x) = x² – 1, and g(x) : -x4 + 1.

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Q: Which of the following represents the area bounded by the graphs of f(x) = x³ – 6x and g(x) = -x² ?…

A: Given 2 functions : fx=x3-6xgx=-x2 We need to show which option represents the area in between the…

Q: Below is the graph of y = a2 +5. 14 12 10 8- 6- 4- 2- -3 -2 -1 1 2 The area bounded by y = x2 +5 and…

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Q: R is the region bounded by x = y? + 1 and x = 9 – y² and the axis of revolution is x = 9.

A: Given that,

Q: The area bounded by the curve y 3x and the lines x = 4 and x = 36 above the x – axis - is O 3888.00…

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Q: Below is the graph of y = z2 +5. 301 2어 1어 -4 -3 -2 -1 0 i 2 3 4 5 The area bounded by y = z2 +5 and…

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Q: The total area bounded by the graph of y = x2 –- 1 and the x-axis is represented by :Select one L…

A: The correct option is d. Plot the curves and find the region for the area between the curves. The…

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: Solve for what is asked. 1. Find the area of the region bounded by f(x) = x³, the x-axis, and the…

A: This question is based on application of Integration.

Q: 2 1. Use Simpson's rule to evaluate | dx , by taking n=4 o V1 + x* 2.Find the Area, enclosed by the…

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Q: Which of the following gives the area of the region between the graphs of y =x2 and y = -x from x= 0…

A: We have to use area between the curve formula.

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.