Find the exact area of the region enclosed by the graphs of x = 9 – y and x = 4. You must show on your work, how you got the bounds and also the Fundamental Theorem of Calculus.

Q: Find the area of the region bounded by the graphs of the given equations. Rou nd to 2 decimal places…

A: Given,

Q: What is the area (in square units) of the region bounded by the graphs of y=x2+2, and the x axis…

A:

Q: Find the total area bounded by y=x^3-3x+2 and y=x+2.

A: Definite integration is one of the methods that can be used to obtain the area bounded by two…

Q: Find the exact area of the region enclosed by the graphs of x = 8 – y2 and x = 3. You must show on…

A: we have to find the area of the region

Q: 4. Find the area of the region bounded by the graphs of y = x3 + 6x, x = 0, x = 2, and the x-axis.

A:

Q: Find the area of the region bounded by the graphs of the equations.              y = 1 − x4,    y =…

A: We sketch the region using a graphing calculator.

Q: Find the exact area of the region that lies under the curve given by y = 10/2x +1, 0<x <1 %3D

A: We know the area of the region that lies under the curve  y=f(x),  a≤x≤b is given by Area =∫aby dx…

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: FIND THE AREA OF THE REGION BOUNDED BY THE FOLLOWING CURVES: 1. y = x(x-3), x = 0, x = 5 2. y =…

A: Given

Q: Find the area of the region bounded by the graphs of the equations y=x−x3, x= 0, x= 1,and y= 0.

A: Given equations: y=x-x3x=0x=1y=0 The region bounded by the graphs is shown below:

Q: Find the area of the region bounded by the curves y = x ^ 3 - 12x, y = x ^ 2.

A: y = x ^ 3 - 12x, y = x ^ 2.

Q: у 3 4/x, у-4y + 2х %3D 5 2x = 5

A:

Q: Find the area of the finite region in the first quadrant bounded above by y=4 and below by y=4x^3

A: Given,

Q: Find the area of the region bounded by the graphs of the equation y = x and y= x².

A:

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

A:

Q: 1. Find the area bounded by y = 4x-x, x+2 = 0 and y = 4 using vertical and horizontal strip

A: Solution is given below:

Q: Find the area bounded by the graphs of y = 3x2; x = 0; x = 2; and the x axis.

A: Given,

Q: Find the area of the region bounded by the parabola y^2=x+3 and the line x - y = -1

A: Given: Parabola: y2=x+3 and line : x-y=-1 To find : Area of the region bounded by the given parabola…

Q: 1. Find the area of the region bounded by the graphs of the equation y = x and y = x2.

A:

Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

A:

Q: Find the exact area of the region bounded by y = -x² + 3x +1 and y = -x+1

A:

Q: 1. Find the area of the region bounded by the curves y = x2 – 3x + 5 and y = 3x + 5.

A: Answer and explanation is given below.. For solution of other questions please repost

Q: Find the area of the region between y=x^1/2 and y=x^1/3 for 0≤x≤1.

A: the area of the region between y=x^1/2 and y=x^1/3 for 0≤x≤1.

Q: Find the area of the region bounded to the right by x = y + 2 and to the left by x = y². 543-2 1…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one…

Q: Find the area of the region bounded by the graphs of the equations y = x² and y = vx.

A:

Q: Find the area of the region bounded by the curves y = -x² – 3x + 4 and y = x2 – 3x – 4.

A: We first sketch the region using a graphing calculator y=-x2-3x+4 (violet) y=x2-3x-4 (black)

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

A:

Q: 2. Determine the area of the region bounded by the curve y = x³ — x² – 2x, and a. the x-axis

A: Given curve y=x3-x2-2x. The objective is to determine the area of the region bounded by the curve…

Q: Solve for the area of the region bounded by: x^2 = 4y + 4 and x = y - 2

A:

Q: What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis from…

A:

Q: Find the area bounded by the graphs of 1, y= and X=1 (Ao the right)

A: Find your answer below

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 of the region bounded by the graphs of y = x +6x, x = 0, x = 2, and the x-axis.

A: Answer

Q: Find the area of the region between the graphs of y = 13 – x² and y = over the interval 3 < x < 8. –…

A: Solve by integration

Q: Find the area bounded by the curves y = 4x, x² =y x=1 and x=4

A: Consider the curves  y2=4xx2=yx=1x=4

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 graphs of the given equations. v= x+2; y= x² 13 O 35 2 o…

A:

Q: find the area of the region bounded by y=(x+2)^2-1, the x-axis, x=-1, and x=2.

A:

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

A:

Q: 2. Find the area of the region bounded by x = y² - 4 and x = 3y.

A: Given query is to find the area of the region bounded by x=y2-4 and x=3y. The rule for integration…

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

A:

Q: The exact area of the region bounded by the graphs of y = x² + 2, and the x – axis from r = -1 to x…

A: Given that:

Q: Find the volume of the area bounded by the curve y²=12x and the line x=3 revolved about x=3

A: Finding the volume of solid generated by given curve

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

A:

Q: Determine the area of the region between the x-axis and the graph of the curv -1 from x- 0 to x- 4.…

A: Area bounded by curves :   If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on a,b…

Q: 1. Find the area of the region bounded by the graphs of the equation y = x and y ?.

A:

Q: Find the area of the region that is enclosed between y=4x^2-x^3+x and y=x^2+3x.

A:

Q: 1. Find the area of the region bounded by the graphs of the equation Y = x and y = x2.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Sketch the region bounded by the graphs of the equations and find its area. y =x² +1; y=x+1

A:

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.