Find the area of the region in the first quadrant that is enclosed by the curves x=y, y=x-, and the x-axis. 3

Q: 21) Find the area of the region in the first quadrant bounded by the line y = 8x, the line x = 1,…

A: We first sketch the region using a graphing calculator.

Q: 9: Find the area of the region enclosed by the curves y x? and x = y about x-axis

A:

Q: Find the area bounded by the lines and curves y = x? - 2 and y = 2

A: Graph:

Q: : Find the area of the region in the first quadrant that is bounded above by y x and below by the…

A: SOLUTION-

Q: Find the area of the region enclosed by the curves y=x+5, y^2=x, y=-1 and y=2

A: You need to draw the graph using the given details and find their intersection points. Then…

Q: 6. Find the area of the region enclosed by the curves x = 3 - y² and x=y_+1.

A:

Q: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

A: the area is given by  A=∫ab|fx|dx................(1) here we have fx=3xex2 the upper and lower limit…

Q: find the area of the region enclosed by the curves y=x^2-2 and y=2

A:

Q: Find the area of the region bounded by y=x^2, the x-axis and the line x=2.

A:

Q: Find the area of the region between y = 5x“ and y = x- + 6.

A:

Q: Find the area of the region in the first quadrant that is bounded above by y = √x and below by the…

A: Now the diagrammatic representation of the area is,

Q: Determine the area of region by y = x^2 + 4x and the y - axis

A: Area between the y=x^2+4x and y-axis is unbounded .  So, we will find the area bounded by the region…

Q: Find the area of the region under the curve y 3x +2x, the x-axis, x=0 and x 4. 0

A:

Q: Find the area of the region bounded by the graph of y = x /(x2 + 1) the x-axis, and the line x = 3

A:

Q: Find the area in the first quadrant bounded by the curves y = x/2, y = 4x and y x2 You need to draw…

A: The graph of the bounded region(shaded region) in the first quadrant is given below.

Q: 3) Find the area of the region enclosed by the curves: y =x, and y = 2x – x

A: For the given curves  y = x2 and y = 2x-x2  Area of the region enclosed by the above curves are…

Q: Find the area of the region between the curves 4x + y^2 = 12 and x =y.

A: 4x+y2=12    and  x=y

Q: Find the area of the region between y² = x and x = y +2.

A: Given,  y2 = x   and  x = y+2  We have to find the area of region between y2 = x   and  x = y+2

Q: Determine the area of the given region. The region in the first quadrant bounded by y 4x and y =…

A: Equate y=4x and y=x25-x2 to obtain the interval of integration.…

Q: Find the area of the region of the enclosed by the curves y = 39 – x² and y = x2 – 33.

A:

Q: Find the area of the region between the curves y = |x| and y = x² – 2. Area between curves =

A: Given : Two curves y = |x| and y = x² - 2

Q: 2. Sketch the region and find the area of the region bounded by y = -x? + 9 and the x-axis.

A: The region is bounded by the curve y=-x2+9=-(x-0)2+9 and the x-axis.

Q: Find the area of the region between the x-axis and the curve y = 8/(x² −4) for x ≥ 4.

A: Integrals and derivatives are considered as the inverses of each other. For example if we have a…

Q: 2 y = x - 3x, y=x 3r.

A:

Q: Find the area of the region enclosed by the curves y = 7 – 2x² and y = x² + 4

A: We need to find the area of the region enclosed by the curves y=7-2x2    and    y=x2+4. Let us plot…

Q: Find the area of the region between the curves 4x + y = 12 and x Area between curves = %3D

A:

Q: Determine the area of the region bounded by the curves y = ₁, y = 2x and x = 4

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: Find the area of the region enclosed by the line y=4x and the curve y= x+ 3x.

A:

Q: Find the area enclosed by the given curves. y = 2x-x2,y 2x-4 31

A: Explanation of the answer is as follows

Q: Find the area of the region bounded by the curves: y = 5x y = 5/x Area = Check

A:

Q: Graph the region bounded by the curves and determine the area of the region. x = y? – 2y; x = 0

A: ANSWER :

Q: Find the total area of the region between the curve and the x-axis. 9) y = (x + 4)3; 0 <x<3

A: The Area Under a curve The area under the curve between two points can be found by a definite…

Q: Find the area of the region bounded by the curves x=y3 and y=x2.

A:

Q: Find the total area of the region between the curve and the x-axis. 7) y = 2x - x2; 0 sx<2

A: Given, The curve  y = 2x-x2   ;  0≤x≤2 We have to find the area of region between the curve and the…

Q: problem in photo attached

A:

Q: problem in photo attached

A: Given:

Q: Find the area of the region enclosed by the curves 4x² + y = 4 and x - y = 1.

A:

Q: Find the area of region enclosed by the curve y = x' -4 x +3 and the line y =3.

A:

Q: 5. Find the area of the region enclosed by y = 4 – x², y = 3x and r-axis.

A:

Q: Find the area of the region in the first quadrant bounded by the line y=5​x, the line x=5​, the…

A:

Q: Find the area of the region above the curve y = x2-6, below y= x, and above y=−x.

A:

Q: Find the area of the region in the second quadrant bounded by y= -x and y=x^4

A:

Q: Find the area of the region bounded by the curve y = 3x -1 and the line y = 74. The area is .

A:

Q: Find the enclosed area by the curve with equation y = x² - 9 and the X-axis in the region [−1, 2] 24…

A: In this question, we want to evaluate the area of the region enclosed by the curves y=x2-9 and X-…

Q: Find the area of the region enclosed by the curves: y = x' – 2x², y = 2x² – 3x

A:

Q: Find the area of the region in the first quadrant that is bounded by y= \x , x- axis and y=x-2.

A:

Q: Find the area of the region between y2=x and x=y+2

A: The area between curves is the area between a curve fx and a curve gx on an interval a, b given by…

Q: Determine the area of the region enclosed by the curves y = 3 VI, y=5– T, X-axis and y-axis in the…

A: The area between the curves y=3-x and y=5-x on interval 4, 5:The area between curves is the area…

Q: 2. Find the area of the region between the curve, x = y² + y −6, y- axis and y=0; y = 3.

A: we need to find the area bounded by the given curves.

Q: Find the area of the region in the first quadrant bounded by the line y = 8x, the line x = 1, the…

A: Intersection Points are:  The line x=1 will intersect the x-axis at (1,0) because y is 0 at…

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.