I- Find the area of the region bounded from the right by the curve x 4-y, from the left by the line y + x -2 and below by the x-axis?

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: Find the area of a region bounded by the curves y=e^(2x) - x^3 , the y-axis and x=1

A:

Q: (13) Find the area of the region between the line y = 2x and the curve y =x² +x-2 %3D

A: The given two curves are y = 2x y = x2 + x - 2

Q: Find the area of the region between the graphs of y = 16 – x and -1< x < 7. 3x 2 over the interval…

A: Given: The functions y=16-x2 and y=-3x-2, To determine: The area of region between the graph of…

Q: 4.) Find the area of the region bounded by the curves y =x- 6x? + 8x and y =x - 2x

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: 3. Find the area bounded on the right by x+y=2, and on the left by y=x and below by x-axis.

A:

Q: Find the area of the region enclosed by the line y=4 and the curves y=e^x and y=(x-1)^2

A:

Q: y2 = 4 – x and y² + y = x + 2

A:

Q: the area bounded by the curves y=2-x2 and y=x2 is

A:

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: 6.(. Find the area of the region enclosed by the curves y = x² +1 and y = x +3.

A: I am solving this in step 2

Q: 26. Find the area of the region bounded by the curve y = 4x – x?, the lines x = 1 and x = 3 and the…

A:

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

A:

Q: Find the area of the region between the curves y = x x-1 and y =-2x+2 from x = - 1 to x= 1.

A:

Q: 1. Find the area of the region between the curves y=x -4 and y=2-x.

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Find the area of the region between the curves y=x^3, y=-x, and y=1

A: Area=14 sq.units

Q: Q- Find the area of the region bounded from the right by the curve x = 4 - y? ,from the left by the…

A:

Q: o. Find the area of the region bounded by the curve y =x csc²x, the x axis 1 and the lines x = 1 =t…

A: Answer and explanation is given below

Q: 3. Find the area of the region bounded by the curves y = 1 (x+1)2/ the x-axis using vertical strip.…

A: Solution :

Q: 1. Find the area of the region enclosed by the line x = 2y and the curve x = y - y?

A: We will find out the required area.

Q: 3.) Find the area bounded by the curve y = 2x and y =x-4 a.) Using Vertical strips b.) Using…

A:

Q: d the area of the region bounded by the curves y = 3x and y = x².

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

Q: Find the area of the region bounded by the curve y=x^3-3x^2+3 and the x-axis.

A:

Q: 8) find the area of the regions bounded by the curves: y=x' +x+2 and y = 2(x+1)

A: since you have asked multiple questions in single request so we will be answering only first…

Q: 2. Find the area of the region enclosed by the curve =x- 4 and y = x - 2.

A:

Q: Find the area of the region between the curves y = x² + 9 and y = 10 + 2x on the interval [-1,3].…

A:

Q: 6. Find the area of the region in the first quadrant bounded on the left by the y- axis, below by…

A:

Q: 3. Find the area of the region bounded by x = 3 – y² and the line y = x – 1. Sketch the graph of the…

A:

Q: 27 Find the area of the region bounded by, b. The curves y=x-5x and y 25-x

A:

Q: 4.Find the area of the region bounded by the curves y = x² – 2x and y = x.

A:

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

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 3. Find the area of the region enclosed by the two curves y = x² and y = -2x² + 3x.

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: Find the area of the region between the curve y = 21-x and the interval -1≤ x ≤ 1 of the x-axis.

A: Given: y=21-x, -1,1

Q: What is the area of the region between y=x²-2x-3 and the x-axis from x=0 to x=4? H

A:

Q: Find the area of the region between the curves y=x(2−x) and y=2 from x=0 to x=2

A: To find the area between the curves

Q: 2. Find the area bounded by curves: a. x = 1 - y² and y = -x - 1. b. x = 0 and x = 25 - y²

A:

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

A:

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 between the curves  y= x2 − 4 and y= 2 − x.

A:

Q: 2) Find the area of the region enclosed between the two curves y = x² and y = -x? + 4х.

A:

Q: 2. Find the area of the region enclosed by the parabola y = 2 – x² and the line y = -x.

A:

Q: 1. Find the area of the region enclosed by parabola y=x an line y = 2.x.

A: Topic:- area under the curve

Q: 5. Find the area bounded by the parabola y = x^2 - 3 and the line y =1.

A: Given problem:- Find the area bounded by the parabola y = x2 - 3 and the line y = 1 .

Q: Find the area R- region in the first quadrant that lies below the curve y=x^2+4 and is bounded by…

A: The given problem is to find the area of region R bounded below by the given curve and the line.…

Q: 3. Find the area of the region bounded by the curves y = x² and y = x/x+2. .

A:

Q: 4 Find the area bounded by the curve y = the x - axis, and the vertical lines x = -2 x²+4 and x = 2.

A:

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.

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.