Calculate the area between the curves y = 7- 2x2, y = x2 + 4, and the x-axis.

Q: Find the area between the curves. y = x2 - 18, y = x - 6

A: y = x2 - 18, y = x - 6

Q: Find the area between the curves. y = x2 and y = - x2+18.

A:

Q: What is the area (in square units) bounded by the curve y' =x and the line x- 4=0?

A:

Q: Find the area between the curves y=3/x, y=12x, y=1/3x, x>0

A: We have to find the area between the curves y=3/x, y=12x, y=1/3x, x>0So, first of all we need to…

Q: Find the area enclosed by the x axis and the curve y= 4-x2

A: Find the area enclosed by the x axis and the curve y= 4-x2

Q: Find the area between the curve y = 6x – 2x and the x-axis between x 1, and x = 3. ||

A:

Q: Find the area bounded by the given curves. y = 3x2 and y = 27…

A: Given:

Q: Find the area between the curve y=4x-x² and the x-axis

A:

Q: Find the area between the curves x² and 3x – 2

A:

Q: find the area between the curves 2x^2+4x+y=0 and y=2x

A: Given that: 2x2+4x+y=0    and   y=2x

Q: Find the area of the curve bounded by the curves y=x* and y=3x+4.

A: We have to find th: e area of the curve bounded by the curves y=x4 and y=3x2+4.…

Q: Estimate the area under the curve y=64-x^3 between x=0 and x=4. Use four rectangles

A:

Q: Find the area between the two curves on [2,3]. y = ex y = (1/x)

A:

Q: Find the area between the curves. x = 0, x = 3, y = 2e3x, y = e3x + e6

A: To find the area between the curves, f(x)=2e3x and g(x)=e3x+e6, use the formula, A=∫ab[g(x)-f(x)]dx.…

Q: Find the area in the first quadrant bounded by the curve y = 3x – x, the lines x = y = 2. 0 and

A: To find the area of the region bounded by the curve we use the formula Area=∫abf(x)-g(x)…

Q: Find the area in the first quadrant bounded by the cubic 3x - x^3 and the lines x = 0 and y = 2.

A:

Q: Find the area between the two curves: y = x2 and y = 4x + 5

A: In this question we have to find Area.

Q: Find the area bounded by the pair of curves. y = x² + 4x and y = 4x + 1 square units

A:

Q: Find the area enclosed between the curve y = 9 - x squared and line y = x + 7

A: This question is based on application of integration.

Q: Calculate the area enclosed between the x-axis and the curve y = x2 - 1 between x = -2 and x = 2.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the area between the two Curves- y=x, a°y = x³ 3,

A:

Q: Determine the area bounded by the curves y = -x² – 16x + 36 and y = (x – 2)².

A: Answer

Q: Find the area between the two curves y = x^2 and y = 2x – x^2

A: Given:     To determine: The area between the two curves.

Q: Find the area bounded by the curve y = 4x - x² and and the lines x = 0 and y = 4. %3D Answer:

A: we can find the area between the curve and the lines by integrating the curve function through lines…

Q: Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

A: We have to find the area between the curve y=x3-6x2+8x and the x-axis.

Q: Find the area enclosed by the curve y = x 2 − 3 and the line y = 2x

A:

Q: Find the area between the curve y = x – and y = -x + 10x2 – 24x 10x + 24x

A:

Q: 2 y = 12 – 3x", y= 4 – x- — х |

A: Let's find.

Q: y = Vx and y = xvx

A:

Q: Find the area between x-axis and the curve defined by   y=2·x2−6·x on the interval [0‍,4].

A:

Q: Find the area between the curves -4x + y = 16 and -2x2 = -y+ 10.

A:

Q: Find the area between the curves. y = x4/3, y = 2x1/3

A: y = x4/3, y = 2x1/3

Q: Find the area between the curves x=y² –1 and x = 2y² – 2.

A:

Q: 2. Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

A:

Q: Find the area above the curve y=lnx in the lower half-plane between x=0 and x=1.

A:

Q: Find the area in the second quadrant bounded by the curve y = x' +4x² – x – 4 and the x – axis.

A:

Q: Find the area between the curves: y=x^3−10x^2+21xx and y=−x^3+10x^2−21x

A:

Q: Find the area between the curves x = 10 − y2 and y = x − 8

A:

Q: Find the area enclosed between the two curves y=4-x^2 and y=x^2-2x.

A:

Q: Find the area between x-axis and the curve defined by   y = 2·x2 − 6·x on the interval [0,4].

A: Given curve: y=2x2-6x We need to find the area between x-axis and the curve on the interval 0,4

Q: Find the area between the curves x2 and 6x – 5

A:

Q: Find the area between the curves y = 4x° and y= 3x + 1.

A: Given the curves y=4x2 and curve y=3x+1. We need to find the area between two curves.

Q: Find the area bounded by the indicated curves. y=7-7x2, y 0

A: We have to find out the area enclosed by the curves

Q: Find the area between the curves y = x and y = -x

A:

Q: Find the area enclosed between the line y 1 and the curve y = x2 – 4x + 4.

A:

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

A: Given data is : y=4x-3     .....1 y=x2      .....2 From equation (1) and (2) ,…

Q: Find the area between the curves. y=x² - 23, y = 9 – 4x

A:

Q: Determine the area bounded by the curves Y = -x² – 18x + 88 and y = (x – 4)².

A: To determine the area bounded by the curves

Q: . Find the area between the curves y =x+1 and y=2x+1

A:

Q: Find the area bounded by the curves, 2x² + 4x + y =0 and y = 2x.

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.