Find the area within the curves y= 25- x', 256x=3y², and 16y = 9x².

Q: Find the area of the region between the curve y 4 In x and the horizontal axis for

A: We have to find the area of the region between the curve  y=4 ln x and the horizontal axis for…

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: Find the area between the curves y – 0.5x = e and y = 2.1x + 1 from x=0 to x=3 Area

A: Explanation of the answer is as follows

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

A: y = x2 - 18, y = x - 6

Q: Find the area bounded by the curve y = x³ − 3x and y + 4 = 0

A:

Q: Estimate the area between the curve y = x^2 - 2x + 5 and the x-axis between x = 0 and x = 3 using 6…

A: Given, y=x2-2x+5 Here, a=0, b=3 and n=6 Therefore, ∆x=b-an3-06=12=0.5 Therefore the intervals are,…

Q: Find the area between the curves. x = 1, x = 2, y = 3x3 + 2, y = 0

A:

Q: Find the area A between the curves y=1+x² y=3+x

A:

Q: Find the area between the curves y and y 3x + 2.

A: From y=x3, y=3x+2 solving for the points of intersections.…

Q: Determine the area bounded by the curves y = -x² – 18x + 63 and y = (x – 3)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 between the two curves on [2,3]. y = ex y = (1/x)

A:

Q: Find the area bounded by the curve: y = 8x – x² and y = 3x

A: a) Consider

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: Determine the area of the region between the two curves by integrating over the y-axis. x = y² and x…

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 curve y=x^2 − 4, the lines y = 0 and x = 4

A: The graph is shown below:

Q: Find the area between the curve y = sin 2x and y = x^2

A: the area is 4/5

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 between the curves. x = -2, x = 4, y = 3e3x, y = 2e3x + 1

A: The above question is from the application of the integration part and since the major part of…

Q: Find the area bounded by the curve y = x² – 3x 3x and y + 4 = 0

A: We have to compute the area of the region bounded by the curve y=13x3-3x and the line y=-4 using the…

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: y = 4 – x2 y = 4 – 4x - -5-

A: Definition used -             The area between two curves f(x) and g(x) -…

Q: 2 y = 12 – 3x", y= 4 – x- — х |

A: Let's find.

Q: Find the area bounded by the curve y = 3x – x3 and the line y = 2

A: Given: y= 3x-x3; y=2 If f(x)> g(x) in the interval x=a to x=b, then the area between two curves…

Q: y = Vx and y = xvx

A:

Q: Find the area between the curves. x = -2, x = 1, y = 2x2 + 5, y = 0

A: Given, x=-2,x=1,y=2x2+5,y=0

Q: Find the area of the region bounded by the given curves. y = 9x2 ln(x),  y = 36 ln(x)

A: First of all, consider the given equations and assume them as f (x) and g (x). Equate f (x) = g (x)…

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

A: y = x4/3, y = 2x1/3

Q: estimate the area under the curve y=x^1/2, from x=1 to x=3 using right end point estimate

A: SolutionGiventhe curve y=x,from x=1tox=3 we need to estimate the area  under the curve y=x1/2,from…

Q: area bounded by the curves y2= 6x and x2 = 6y?

A: Given curvesy2=6x or y=6xand6y=x2 or y=x26

Q: Find the area between the curves y = e 1. = y = 2.3x + 1 from x = 0 to x = Area -0.4x and

A:

Q: Find the area between the curves. x= 0, x= 3, y=2 eX, y= e³ 3x + e

A:

Q: Find the area between the curves y = x2 - 8 and y = 4 - x.

A: Explanation of the answer is as follows

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 y = and y 3x +2. %3D

A:

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

A:

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 = 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: Find the area bounded by the curve x = y^2 + 2y and the line x = 3

A:

Q: Find the area between the two curves y = 3 y = x² – 1 1+ x2'

A:

Q: Find area of the region under the curve y=8−3x^2 and above the x-axis

A: First we find where y=8−3x2 cuts x axis. We set y=0 and solve for x

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 -16 = 4x- y and -10 = 2x-y.

A:

Q: Find the area bounded by the curve and y+ 4 = 0 y=x²-3x 3X

A:

Q: y = 3x2, y = 0 and x 31

A:

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

A:

Q: Find the area of the region between the curves y = sin(nx/2) and y = x. Area between curves =

A: In the question it is asked to calculate the area between two curves y=sin(πx2). and y=x.

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.