Sketch the curve y'(4– x)= x' and find the area bounded by it and x = 4. A = 12T

Q: /Find the area under the curve y = sin x cos 2x from x=0 to x =-

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 2. Find the area in the third quadrant bounded by the curve x= y2 + 2y.

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Q: 2. Find the cerntroid of the area bounded by the curve y= 2x + 1 x+y =7 and x= 8

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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 of the region between the curves y = sin(x), y = sin(2x), x = 0, and x = t/2. Area…

A: Given curve is : y=sinx   .......(1) y=sin2x   ......(2) To find the area of region between curve…

Q: 6. Find the area bounded by the curve 2y² + 4x + y = 0 and the line y = 2x.

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Q: Solve for the moment of inertia with respect to the y-axis for the area bounded by the curves, y? =…

A: follow next step

Q: 3. Find the area bounded by the curves x2 + y2 = 9 and 4x2 + 9y² 36, on the first quadrant.

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Q: x = y² and the line y = x − 2

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Q: Find the moment of inertia with respect to x-axis of the area bounded by the parabola y = 4x and the…

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

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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: calculate the area between y=x^3 and its tangent at the point (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: 2. Find the area between the curves y = Vr -1 and r - y = 1.

A: Given curve is y=√(x-1) and y=x-1

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: Make a sketch to show a case in which the area bounded by two curves is most easily found by…

A: To graph: The sketch to show a case in which the area bounded by the two curves is most easily found…

Q: Find the area between the given curves: f(x) = sinx g(x) = cosx on the interval (0, π)

A: Sketch the region bounded by the curves fx=sinx  and  gx=cosx   on 0, π as shown below.

Q: 2. Find the area between the curve y=-x and y+x²= 2x.

A: The given curves are y=-x and y=2x-x2.

Q: Find the area under the curve y = 5xe-* for x > 0. %3D area %3D

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Q: I. Find the area bounded by the curves y=x', y 1, and x = 0 using double integration.

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Q: Approximate the area under the curve y = x' from z = 2 to a = 4 using a Right Endpoint approximation…

A: To approximate the area under the curve y=x3 from x=2 to x=4 using a Right Endpoint approximation…

Q: Find the line y = mx that divides the area under the curve y = x(1 − x) over [0, 1] into two regions…

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Q: y = e²x and x - 2y + 5 = 0

A: I am attaching image so that you understand each and every step.

Q: Find the area bounded by the curves y= sin 2x and y=cos 2x in 0,

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

A: the area is 4/5

Q: Find the moment of inertia with respect to the x-axis of the area bounded by the parabola y2 = 4 and…

A: Solution is given as below:

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

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Q: Find the moment of inertia of the area bounded by the curve x2=4y, the line y=1 and the y-axis on…

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Q: Find the area bounded by the curve x = cos(t), y = e', 0sts and the lines y = 1 and x = 0. 2

A: The solution are next step

Q: Find the moment of inertia of the area bounded by the curve x^2=8y, the line x=4 and the x-axis on…

A: Use moment of inertia concept

Q: Find the area between the curve inclosed by the curve x = 2y^2 and the curve x = 4 + y^2

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Q: Find the area bounded by the curve 5y^2 = 16x and the curve y = 8x – 24.

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Q: Find the area bounded by the curve y=x³, x=0, y=1 is revolved about the x axis.

A: The graph of the curves is

Q: Approximate the area under the curve y=4x2+1 on the integral [0,4] n=4 using the trapezoid rule

A: Given : y = 4x2 + 1  To find : Area under given curve using trapezoid rule . Solution : Approximate…

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

A: Given function

Q: What is the area under the curve y = cosx over the interval [0 ,π/2]?

A: Integrating the equation of curve in the given interval gives the area

Q: 4. Find the area bounded by the curve r = 3y – y? and the line y + x 3.

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

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Q: Find the area under the loop of the curve y2=x4(x+4) using integration

A: An integration formula for calculating the area under the curve will be used. We will calculate the…

Q: Find the moment of inertia of the area bounded by the given curves with respect to the specified…

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Q: Sketch the region enclosed by the curves 4x+y2=12 and y=x then find its area using the appropriate…

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Q: Sketch the region enclosed by the curves y=2 and y =-2x+3 then find its area using the appropriate…

A: Consider the following curves: y=-2x+3y=2 Intersection point of curves: -2x+3=2-2x=-1x=12…

Q: Find the area of the surface obtained by rotating y = cosh x over [−ln 2, ln 2] around the x-axis.

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Q: Find the area between the curve y = 1/x7/6 and the x-axis from x = 1 to ∞

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

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Q: Find the moment of inertia of the area bounded by the curve x^2=4y, the line y=1 and the y-axis on…

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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: Calculate the area of the following regions bounded by the curve y = 2 - and x = 2y2.

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Q: Find the area bounded by the curve x^2=4y+4 and the line y=x+2

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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.