Let R be the region bounded by the curve y = r and the line y = 2x. Use inequal- ities to describe R in terms of its vertical cross sections.

Q: Sketch the region bounded by the given curves, then find its area. x=y2, x=y+6

A: Here we have to sketch the region bounded by the given curves.  We have, x=y2, x=y+6

Q: Sketch the region enclosed by the given curves. x = 3y2, x = 4 + 2y2 y y 12 10 8 6 6 8 10 12 2 1 2 y…

A: The region is enclosed by the curves,x=3y2, x=4+2y2

Q: Let IR be the region in the first quadrant bounded by the curves y = x3 and y = 2x – x². Compute the…

A:

Q: Sketch the region bounded by the graphs of the equations f(y) = y2 + 1,        g( y) = 0, y = −1, y…

A:

Q: Find the area of the region bounded by the curve y2= 4x and the lines x = 1 and x = 4. O 21/2 square…

A: Here is the solution

Q: Sketch the region enclosed by the following curve and find its area. x = y^4, y =√2 − x, y = 0

A:

Q: Find the number k> 0 such that the region bounded by the curves y = x² and y = kx has area 9 square…

A:

Q: Let R be the region bounded by y = 5 sin(x , y = 5(x – 2)²,

A:

Q: Describe the region R bounded by the curve y = x² and the line y = 2r in terms of inequalities using…

A:

Q: Let R be a region bounded by the curves y = x² and y = 4x – x². Evalua /| (a + y)dA. R

A:

Q: Sketch the region enclosed by the given curves. y- Vx- 3, x - y - 3

A: To find the area of enclosed region of the given curves, first we find the intersecting points of…

Q: Sketch the region enclosed by the given curves andfind its area.   y  = 1/x,  y =x ,    y =1/4x  ,…

A: y  = 1/x y =x     y =1/4x and x>0 Formula: Area enclosed between the curves y=f(x) and y=g(x) on…

Q: Sketch the region enclosed by the given curves. x = 7y2, x = 4 + 6y2

A: Here, We will use the concept of tracing the simple curve, and method of double integral to find the…

Q: Sketch the region enclosed by the given curves. y = 3/x, y = 12x, 1. y = -X, 3 x >0 y y 8- 6. 6. 4 4…

A: Given curves: y=3x, y=12x, y=x3 Andx>0

Q: Sketch the region bounded by the given curves, then find its area. 1. y = x², y = 2x

A:

Q: Find the number  b such that the line  y = b divides theregion bounded by the curves y = x 2  and y…

A: Given Data The equation of curve is y=x2. The equation of line is y=4. The equation of another line…

Q: Let R be the region bounded by the curve y = x and the line y = 2x. Use inequal- ities to describe R…

A: To describe: The region R using inequalities in terms of its vertical cross-sections. Calculation:…

Q: The value of $ $(2xy - x²) dx + (x+y2) dy, where C is the enclosed curve of the region bounded by…

A:

Q: The region R is bounded by y 4 %3D and y = x +3. -

A:

Q: Sketch the region bounded by the given curves, then find its area. y = x^2, y = 2x

A: Given,            The equation of the curves are y=x2 and y=2x.To find : Find its area.

Q: Given that R is the region bounded by the curve y = x+3 and line y= x-3. (b) Describe the region Rby…

A:

Q: consider the region in the xy plane bounded above by the curves y=x9/2 and y=x

A:

Q: (1) y = x, y = 2- |x| (2) y = 1/x², y = 8x, y = x/8

A:

Q: Sketch the region enclosed by the curves/lines x = y, y =1/x, x = 3 and find its area.

A: given,         x=yy=1/xx=3

Q: Let R be the region in the first quadrant bounded by the curves y = x³ and y = 2x – x² Compute the…

A: Volume about y-axis

Q: Let S be the region bounded by the curves y = x and x = y²/2.

A: (a) Area of region bounded by given curves, S=∫02(2x-x)dx    (Area= ∫abf(x)-g(x)dx)

Q: Sketch the region enclosed by the given curves andfind its area.       y +x = 3     , y = 2  x 2  ,…

A: The given curves are x+y=3 , y=2x2 and y=14x2 , x≥0. To sketch the curve and find the area. The…

Q: Sketch the region enclosed by the given curves. y =- y = 8x, y = x > 0 y y 6 4 3 3 2 1 1 X 2 4 -1 3…

A: Given that the curves are      y=2/x , y=8x , y=x/8 , x>0 Here we have to sketch the region and…

Q: Let R be a region bounded by the curves y = x2 and y = 4x – x2. Evaluate | (x+ y)dA. 2.

A: When a function of two variables is integrated over a region, the double integral is used. It is one…

Q: Find a vertical line x = k that divides the area enclosed by x = y , x = 2 , and y = 0 into two…

A:

Q: Find the centroid of the region bounded by the graphs of the inequalities

A: Given information: y≤14x2          ...(1)x-42+y2≤16              ...(2)y≥0                ...(3)

Q: Sketch the region enclosed by the given curves andfind its area.    x = 2 y 2  , x =  4 + y 2

A: Definition used -    The area between curves -                        A=∫ab(f(x)-g(x))dx

Q: Let R be the region bounded by the curves y=x^2 + 1 and y= 9 - x^2. What is the area of R?

A: Follow the steps.

Q: Sketch the bounded region enclosed by 2y = 4/x, y = 3, and 2y + 3x = 7, then %3D find its area.

A:

Q: Sketch the region enclosed by the given curves. y = V5x, y=x

A:

Q: Evaluate where D is the region bounded by the semicircle x = /4– y² and the y-axis.

A:

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given,    y = x,  y = 4  and  x = 0 So the region bounded by these curves is given by shaded region…

Q: Sketch the region enclosed by the given curves. y = 4/x, y = 16x, y =x, x>0 16 y y 10| 10- 8 6. 2 4…

A:

Q: Sketch the region enclosed by the given curves. y =2 y= 8x, y= 극x, x > 0 y 5 4 3 2 1 -1. 1 3 2.

A: Given: y=2x, y=8x, y=x2, x>0

Q: R is the region bounded by the lines y = x, y = -x, and x = 1. %3D

A:

Q: Determine the absolute maximum and minimum values of f(x, y) = 2+4x-2.x2+4y-y? %3D on the region R…

A:

Q: Sketch the region enclosed by the given curves. y = ex, y = x2 – 4, x= -2, x = 2

A:

Q: Using your previous work, find the region bounded by the curves y = x² and y = x³.

A: Given that, There are two curves following, y = x2  and   y = x3 We have to find the area bounded by…

Q: Define the region bounded by y = 0, y=4Vx , y = 24 - 2x and y = X -4 using vertical and horizontal…

A: The equations of the bounding sections are: y=0y=4xy=24-2xy=x-4 The equations are plotted on a…

Q: ) Find the number k>0 such that the region bounded by the curves y = x² and y = kx has area 9 square…

A:

Q: Sketch the region enclosed by the given curves. y = 4/x, y = 16x, y = x, x > 0 16

A: We have the following equation   y=4xy=16xy=116xWhere x>0 First, we will make a table for each…

Q: The lower, upper limit in the evaluation of the area of the region bounded by the two curves y = and…

A: Given curves are: y=x2 ............(1)y=10x-16   .........(2)

Q: define the region bounded by y = 0, y = 4√x, y = 24 − 2x, and y = x − 4 using vertical and…

A: Given curves are y=0, y=4x, y=24-2x and y=x-4. We have to define the region bounded by the given…

Q: Consider the region bounded by the curves y= X,y= 3-2x, and y=3 %3D

A: 1) Shaded the region :

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.