Q1) graph the curve r= 4sin (20).

Q: Find the exact length of the curve. x- 2, y=? - 2, Osts 6

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Q: |-*^= 39. What is the length of the curve y = √x- between x = 0 and x = 2?

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Q: 3n Q10:- Show that the point (2,) lies on the curve r=2sin 20. 4

A: 10) Given curve is r=2sin2θ show that (2,3π4) is a point lies on the curve

Q: 7-18 - Find the exact length of the curve. 7. y = 1 + 6x³/², 0 < x < 1

A: We find y' using the power rule

Q: 7. Find the exact length of the curve: y = 1 + 6x³/², 0 < x < 1.

A: The length of the curve is calculated from the graph.

Q: Find the exact length of the curve. 0 < x < 6 %3D 3

A: Given:   To determine: Exact length  of the curve     Concept: Exact length of the curve y = f(x)…

Q: 3/2 Find the length of the curve. y = (x* +4)" OSxs2

A: see below the answer and calculation

Q: Find the exact length of the curve. x- 2, y =? - 2, Osts9

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Q: Find the exact length of the curve.

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Q: Consider the curve y = 3x3, The sketch of the portion of this curve between x = - 1 and x = 8 is…

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Q: Find the exact length of the curve. y 1x²-1-In(x), = 4 2 1 ≤ x ≤ 8

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Q: Find the exact length of the curve. = 플Vy (y-3), 4sys 16 3

A:

Q: Find the length of the curve r=θ^2 from θ=0 to θ=6

A: Given: -

Q: Find the exact length of the curve. x = et − 9t,    y = 12et/2,    0 ≤ t ≤ 2

A: Note that:Arc length formula = ∫abdxdt2+dxdt2 dt                   where , a≤t≤b       Given,…

Q: Find the exact length of the curve.   36y2 = (x2 − 4)3,    5 ≤ x ≤ 6,    y ≥ 0

A: NOTE: Refresh your page if you can't see any equations. . but here

Q: Find the exact length of the curve. 36y2 = (x2 – 4)³, 4 < x < 9, y 2 0

A: Given:

Q: Find the exact length of the curve. y = 5 + 2x³/2, 0< x < 1

A: Given: y=fx=5+2x32, 0≤x≤1 we know that lengthL of curve in interval a,b is given by L=∫ab1+f'x2dx…

Q: The graph, when the curve y=v(3+ x^2 ) from x = 0 to x = 4 is rotated about x - axis is ....

A: This question can be solved using the concept of volume of solid generated when curve is rotated…

Q: Sketch the graph of the curve r = 2+4Cose

A: Given equation: r=2+4 cos θAmplitude: 4This equation will have the same time periodas sinθ which is…

Q: 25 Which of the following is the shortest distance from the point to the curve y = v5x?

A: We have to find the expression of distance using parameter.

Q: Find the exact length af te of the curve, 2. x-

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Q: Find the points on the curve y = 14x closest to the point (0, 1). and

A: This question is based on application of Derivative.

Q: (b) Eliminate the parameter to find a Cartesian equation of the curve.   for  −5 ≤ y ≤ −1

A: The parametric equation of curve are x=1-t2 y=t-3

Q: Find the exact length of the curve. y = x3/2, osxs 6 3

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Q: Find the length of the curve from the entire hypocycloid 2 2 x3 + Y³ = a³.

A: Explained below

Q: Find the length of the curve x = - (5 + 4t), y= 1- t, z= - (4+ 2t), for 3 <t < 5. length = (Think of…

A: Find the length of the given curve.

Q: The family of curves orthogonal to x2 + 4y2 = c2 has the general equation 04. %3D

A:

Q: Explain the steps required to find the length of a curve x = g1y2 between y = c and y = d.

A: It is given that x=gx for c≤y≤d.

Q: 5y=4 How would I make this into y=mx+b and graph this?

A: Consider the given equation,5y = 4Convert the above equation in form of  y = mx + b,

Q: Find the length of the curve y=x^3/2 from (1,1) to (2,2squareroot2)

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Q: 9y? = 4x3 from the origin to the point (4, %3D 144. Identify the length of the curve

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Q: 7.) Find the shortest distance between (4,2) and the curve y? = 8x.

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Q: 1. Find the length of the curve 4Y, 1<Y<2 8

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Q: Q1/ Find the equation of the circle tangent at least to three lines (y = 1, y 5, x 2 and x = 7). %3D

A: We have considered the first 3 lines as the line of the tangents For more see below

Q: Find the points on the curve y 13x closest to the point (0, 5). )and (

A: Topic:- point  on the curve

Q: Sketch the curve with equation x2/3 + y2/3 = 4 and use symmetry to find its length.

A: Arc Length formula in the interval [a,b] is given by, L=∫ab1+dydx2 dx This is applied only when dydx…

Q: Find the exact length of the curve. 36y2 = (x² – 4)3, 2 < x < 9,

A: Given:  36y2 = (x2 - 4)3 , 2≤x≤9,y &gt;= 0

Q: At what part of the curve 2x2 + y? = 8 does it assume the highest value?

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Q: Find the shortest distance from the point (4,2) to the curve x^2 Зу^2 %3D 12 +

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Q: Sketch the curve with equation  x2/3 + y2/3 = 1  and use symmetry to find its length.

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Q: 1 + 12 8x*' - Find the length of the curve y= 1<x<2. 4

A: y=x612+18x4 Differentiate the  above equation dydx=ddxx612+18x4dydx=x52-121x5

Q: Find the exact length of the loop of the curve = 3t – t°, y = 3t2 -

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Q: / Find the length of the curve y = (÷) (x²

A: Given,         y=13x2+232

Q: The given curve is rotated y = 3 - x2,

A:

Q: A curve C has equation y =x2lnx- 2x +5, x > 0. %3D For which values of x, the curve C is convex?

A: The equation of the given curve is  y=13x2 ln x-2x+5 , x&gt;0 For the curve to be convex its second…

Q: i) Find the exact length of the curve y=+15x52 4x3 1 ≤ x ≤ 2,

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: 5. The coordinates of the vertex of the curve y = 1- 2x - 4x² are: A. G ) B. (- 5 ) €(- ) D.(- -) 1…

A: Hi, for question 6 repost

Q: The length of the curve 4/2 3 y = xi - 1,0 < x < 1 is .

A: Given,            The length of the curve y=423x32-1 , 0≤x≤1 is 136.To find : Check whether the…

Q: d the exact length of the curve. =√y (y - 3), (y - 3), 4 ≤ y ≤ 16

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Q: =+ dr x = 2 ke x = 3 16 2x2

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.