Determine the exact area enclosed between the two curves y = (x)^1/2 and     y = 1/2(x)

Q: y = ln x and x - y -4 = 0

A: Explanation of the answer is as follows

Q: Find the area bounded by the curve y = x2, AB is tangent to this curve at point P (2,4) and the x-…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Find the area of the region bounded by the parabola y=5x^2, the tangent line to the parabola is at…

A:

Q: Find the area between the curves y = 4 cos(6x),    y = 4 sin(12x),    x = 0,    x = π/12

A: Given,

Q: Find the area between y=x+2 and y= x2−1. Round your limits of integration and answer to 2 decimal…

A:

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 exact area between the curves y =x´ and y = 2 - x. %3D

A:

Q: Find the area bounded by the curves an arch of y= (4)sin (xA)

A: Given:        y=14sinx4 The area under the curve is the area between a curve f(x) and x-axis on the…

Q: Find the area between the curve y=x^3 and its tangent through (1,1)

A: The slope of the tangent is given by y' at (x,y)=(1,1) y'=3x2At x=1y'=3 Equation of tangent line is…

Q: Find the area enclosed by the curve y=(x)^1/2, the tangent to the curve at x=4 and y axis.

A: Consider the provided information, y=x12 The tangent to the curve at x=4 and y axis. Find the area…

Q: Determine the area bounded by the curves y = -x² – 18x + 63 and y = (x – 3)². |

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

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

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Q: The area between y= 2sinx and y = sin2x for 0<x ST is

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Q: Determine the area bounded by the curves x^3 - y = 0 and y + 3x^2 - 4 = 0 using a vertical element

A: The area is bounded by the given curves x3-y=0 and y+3x2-4=0. The main objective is to determine the…

Q: 4 y = 1 + x4' y = 2x2

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Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4 and provide a correct and…

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Q: Find the area bounded by the curve y (x- 2)(x + 1)(2x – 1) and x-axis.

A: We use integration to find the area.

Q: Find the area of the propeller-shaped region enclosed by the curve x - y3 = 0 and the line x - y =…

A: x-y3=0  &amp;  x-y=0⇒y3=x  &amp;  y=x⇒y=x13  &amp;  y=x Now the diagrammatic representation of the…

Q: Two curves having an equation of x = 2vy and y = 2Vx intersect each other. Compute the area between…

A: Solution:-

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

A:

Q: y = 4 – x2 y = 4 – 4x - -5-

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

Q: Find the area of the loop of the curve y2=x3 (1-x)6. Show complete solution of points of…

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Q: When we find the area between an upper curve f(x) and a lower curve g(x), we integrate f(x)-g(x).…

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

A:

Q: The area under the curve y = cos x from x = a to x = is 0.2. What is the value of a 2 rounded to…

A: Area under a curve y(x) is given by ∫abydx         where a≤x≤b

Q: Find the area bounded by the curve y = 9 – x2 and the x-axis.

A: Area

Q: Evaluate the definite integral that represents the area of the surface generated by revolving the…

A: to find:- surface area of revolution about x axis.

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: Two curves having an equation of 2y² and y = 2x² x = intersect each other. Compute the area between…

A: A detailed solution is given below.

Q: Use the method of anti-derivative to find the area under the curve y = 4(x³ the interval [2,4]. 4x)…

A: Before finding the area, first, we will find the x-intercepts of the curve  to check that any point…

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

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Q: Find the area under the curve y = sin √x /√x between x = π^2/4 and x = π^2

A: Given function

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

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Q: Please use definite integral in solving for the area. y = |x| – 2 and the x axis

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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: Find the area between the curves y 0.7x and y = 2.4x +1 from x = 0 to x = 4. = e Area =

A:

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

A:

Q: Sketch the region bounded above by the curve 7e- sin(Tx), the x-axis, and x = 1, and find the area…

A: Given,

Q: Find the area bounded by the curve y= 2x-3/x2+4, the coordinate axes and the minimum ordinate. Show…

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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: Find The Area Enclosed by the Curve x=7²-2t,y-VE and the Y-pris

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 of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

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Q: Find the area bounded by the curve y^2 + x - 4y = 5 and the y-axis. Input only the numerical value…

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Q: Find the area between the curves. 3x 3x x-0, x-D4, y3D2e" y-e

A:

Q: Sketch the region in the first quadrant bounded by the curve x+y2=4, and find its area first by…

A: To graph the function, solve the given equation for y. Since the region is in the first quadrant,…

Q: | x(1 – x)9 dx

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.