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

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: 1/ Find the area of the region enclosed between the curves y= 2r'+10 and y=4x+16 and ,x=-2 and x=5?…

A: The area of the region enclosed by the given curves has been obtained below.

Q: Find the area between the curves y=e^−0.7x and y=2.1x+1 from x=0 to x=1. Area=_____

A: Using Formula of Area between two curves.

Q: 12. Find the area of the region enclosed between the curves defined by the equations y = √(x + 2), y…

A: We have to evaluate the area of the region bounded by the curve y=x+2 and the line y=x using the…

Q: Find the area between the curves y = e-0.7x and y = 1.5x + 1 from x = 0 to x = 1.

A: Explanation of the answer is as follows

Q: Determine the area of the region between the following curve. x = |y| and 2x = −y^2 + 2

A: Given that, x = |y| and 2x = −y2 + 2

Q: Find the area between the curves y=e^−0.6x and y=1.6x+1 from x=0 to x=1

A:

Q: || 2. Find the area of the region enclosed by the curves x = 2y² – y + 1 and x y² + y + 4.

A: The area between two curves is given by: Where a and b are intersection points of the curves f and…

Q: Find the area between the curve  y = x2 + 3x + 2  and the x-axis from  x = −1 to x = 1.

A: We have to find the area between the curve y=x2+3x+2 and the x-axis from x=-1 to x=1.

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: B- Find the area between the curve (y-√x - 2) and the lines (y-4-x),(y=0).

A: We have given three curves-y=x-2y=4-xy=0 First we will find intersection of first two curves…

Q: 1. Find the area between the curves x2-y = 9 and the line y 2x-6

A: Since you have posted multiple questions in this question which are not interlinked so I do only…

Q: 1. Find the area between the curves of y = x2 +1 and y = x +7 from x = -2 to x = 3. Round to two…

A: Topic-application of integration

Q: 1. Find the area between the curves x2-y2 = 9 and the line y = 2x-6

A:

Q: 2. Find the total area of the region between the curves y = sinx and y = cosx for 0<xs 37 2

A:

Q: Find the area of the region bounded by the curve y2-4r and the lines x = 1 and x = 4.

A:

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

A:

Q: 1/ Find the area of the region enclosed between the curves y= 2r²+10 and y=4x+16 and ,x=-2 and x-5?…

A: Given          y=2x2+10    and  y= 4x+16,   x=-2 and   x=5.

Q: 1/ Find the area of the region enclosed between the curves y= 2x2+10 and y=4x+16 and ,x=-2 and x=5?…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

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 between the curves: y2=x x2– 2x + 3y = 2

A: we have to find the area between the curves :

Q: Find the area between the curve y=2x+4x-6 and the x-axis from x =-2 to x= 3.

A:

Q: 2. Find the area between the curves. x = - 2, x = 1, y = 6x, y = x2 - 7

A: Given: x=-2,x=1,y=6x,y=x2-7

Q: Find the area between the curve y = x2 + 10x + 16 and the x-axis from x = −2 to x = 1.

A: We have limits of curve from x=-2 to x=1

Q: 14. Find the area of the region bounded by these two curves: X = y' – 2y and x-y-4=0

A:

Q: 8. Find the area between the curves y = x x² and y = x2 – 4x between x = O and x = 2.

A: For calculating the area between curves first of all we will draw the schematic diagram of the…

Q: 1) Find the area of the region bounded by the curve y=3x•e-2* and the x-axis, for x>0. i) Rou imal

A:

Q: 7. Find the area of the region under the curve y= |2x – 1| between x= O and x= 2.

A:

Q: Find the area between the curves: y=x^3-11x^2+18x and y = -x^3+11x^2-18x

A: y=x3-11x2+18x and y=-x3+11x2-18xTo find the area between the curves:

Q: 4. Find the area of the region bounded by the curves x-y² = 0 and x+2y² = 6.

A: Hence, the area of the region bounded by the curves x-y2=0 and x+2y2=6 is 82 square units .

Q: Find the area of region bounded by the curves x= 2y+6 and x y-1.

A:

Q: Find the area between the curves y = e – 0.4x and y = 2.1x + 1 from x = 0 to x = 4. Area =

A:

Q: problem in photo attached

A: Consider the given functions:

Q: Find the area of the region lying between the æ- In(9x) – 1 axis and the curve y = to the right x2…

A: Solving by area formula

Q: 1. Find the area between the curves of y = x² + 1 and y = x + 7 from x = -2 to x = 3. Round to two…

A: (Note: We are entitled to solve only one question at a time) Given: y=x2+1 and y=x+7 x=-2 , x=3. To…

Q: Find the area between the curves y = x² + 5x and y = 3– x² between a = -2 %3D and z = 0.

A:

Q: Find the area between the curves. y = x2 - 9x + 4 and y = x² + 6 from x = 0 to x = 6

A:

Q: Find the area of the region between the curves x=((y-2)^2)/3 and y=8-x shown in the following…

A: Explained below

Q: 1. Find the area between the curves x2-y 9 and the line y 2x-6 %3D

A:

Q: 1.) Find the area of the region bounded by the parabola y = 2x and the line y = x - 4

A:

Q: 5) Calculate the area of the region between the curves: y=2-x² and y=x²

A:

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

A:

Q: 5) Calculate the area of the region between the curves: y = 2 = x² and y = x²

A: We can find the area as below.

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 graph of the given curves and find the area of the region bounded on the left by the…

A: Graph of x=3-2y2, that is gy=3-2y2 is a parabola as function g(y) is in the form of quadratic…

Q: Find the area of the region under the given curve from 1 to 2. 13 y = x + 4x

A: As we can calculate the area under the given by integrating the given function for the given…

Q: 18. Find the area of the region enclosed by the curve y = (1- x)²; 0<x< 1. (in QI)

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.