C3. Find the length of the of the curve x= 1 from y = 1 to y = 2 %3D 4 8y?

Q: Given dy (1 + 3 k). dx 13 2 What is the value of k such that y is parallel to the curve y = 3x +1 at…

A: Given,            dydx=2131+52x-32-34k            The curve is y=3x+1 at x=1.To find : The value of…

Q: 48. x = e' – t, y= 4e"², 0<t<2

A:

Q: Q6 Find the length of the arc of the curve in the given range, y3 4(у + 4)' 1 х %3D 16у + 4у? + 3 0…

A: Find the Arc length

Q: 4/2 % for 0 sxsl. Find the length of the curve y+1=- 3

A: The equation is y+1=423x3/2.   Differentiate with respect to x.…

Q: 7) Find the exact length of the curve. x= e' +e', y =5-2t; 0<t<3

A: Solution:Givenx=et+e-t     y=5-2t     0≤t≤3To find the length of the curveFormula:Length of the…

Q: The length of the curve y= is equal to x =3: from to 을(x2 + 2) O a. 12 Ob. 1 O c.9 Od. 3

A: We can use the application of integration in order to solve the given problem.

Q: Q2: Find the length of curve: x = cost, y = t+ sint, 0st<.

A: The given curve is: x=cos t ,       y=t+sin t ,        0≤t≤π

Q: (b) Find the value of k for which 2y +x k is a tangent to the curve y +4x 20. %3D

A:

Q: 1 Find the length of the curve x= from y 1 to y=2. +. 16y

A:

Q: Find the curve length of the given functions in the given interval

A: Find dx/dt and dy/dt using product rule.Then find (dx/dt)^2 and (dy/dt)^2.

Q: dy d²y Find and dx dx2 x = t? + 8, y = t2 + 5t dy dx d?y dx2 For which values of t is the curve…

A: will be concave upward for all t belongs in [-1,-inf)

Q: Q6 Find the length of the arc of the curve in the given range, y3 1 16y + 4y2 + 3 x = 4(у + 4) + 4)…

A: Find Arc length

Q: The line y = mx + 1 is a tangent to the curve y2 = 4x .Find the value of m

A:

Q: Find the exact length of the curve x = tsint, y = t cost where 0 ≤ t ≤ 1.

A: answer is in next step

Q: y = 1/2 (e² + e^¹), − 1 ≤ x ≤1

A:

Q: a)Find the exact length L of the curve 3y? = (4x – 3)°, 1 0. Answer: b) Evaluate Sxe*dx Answer: 1 c)…

A:

Q: Find the exact length of the curve y=1+6x% for 0<xsl

A: We have to find the exact length of the curve y=1+6x32 for 0≤x≤1.

Q: 3. Find the length of the curve r = e® for 0ses 2n.

A: Given polar curv er=eθ   ; 0≤θ≤2π

Q: e length of the curve y = V 4 – x2, 0 <x< 2. ing the shape of the curve.

A: Use the arc length formula to find the length of the curve.  y=(4-x2)1/2 , 0&lt;=x&lt;=2

Q: Find the length of the curve. V2 ti + e'j + e-tk, 0 <t< 8

A:

Q: Find the exact length of the curve for the parametric equation

A: Let's say the length of the curve is L.  0 ≤ t ≤ 1 Hence, the desired length will be calculated as:

Q: Find the length of the curve. r(t) = (4t, 0 <ts 1

A:

Q: a)Find the exact length L of the curve 3y = (4x – 3), 1 0. Answer: b) Evaluate xe*dx Answer: .3 c)…

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: Find the point on the curve y = Vx closest to the point (1,0).

A:

Q: y = e*, 0<z<1.

A:

Q: Q5 Find the length of the arc of the curve in the given range, y3 3 ' 4(y + 5) 1 x = 25y + 5y2 +…

A:

Q: Find dy/dx and d²y/dx². x = e', y = tet dy dx dy dx2 For which values of t is the curve concave…

A: Given a parametric equation,

Q: Find the exact length of the curve. 36y =(x+4). 5 5 x s 6, y 20

A: Given: 36y2=(x2-4)3,  5≤x≤6,  y≥0 Arc length of curve y=f(x) on [a, b] can be calculated by…

Q: Find the length of the curve x = (y3/33) + (11/4y) on 3≤y≤5.

A: Consider the given curve f(y) and find the derivative w.r.t y.

Q: Find the exact length of the curve given by a = t° ,y (0 <t< 4). Length =

A:

Q: Find dy/dx and d?y/dx2. x = t2 + 4, y = t2 + 3t dy dx d?y %3D dx2 For which values of t is the curve…

A: Let's find.

Q: For the implicit curve y + xy + x2 = 3, find a point on the curve where the tangent line is…

A:

Q: Find dy/dx and d²y/dx². dy dx d²y dx² 11 || x = t² + 9, y = t² + 3t For which values of t is the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the exact length of the curve (a) x = 1+ 3t2, y = 4+ 2t³, 0<t<1 (b) x = e' cost, y = e' sin t,…

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

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: 49 sec t – 1 dt with 3 Find the length of the curve x = Length is

A:

Q: Find dy/dx and d?y/dx2. x = t2 + 9, y = t2 + 5t %3D dy dx d²y dx2 %3D For which values of t is the…

A:

Q: Find the length of the curve. y 3x 3/2 from x = 0 to x = О 335 162 О 335 O 1 O335 243 559 3.

A:

Q: (c) Find the length of the curve described by r = e30 for 0 < 0< 4.

A: Given, r=e3θ for 0≤θ≤4

Q: Q.N.4 Find the length of the curve 3x = (y + 2)3/2 from y = 2 to y 3 %3D

A:

Q: Q6 Find the length of the arc of the curve in the given range, y3 x = 16y + 4y² + 0<y< 4 %3D 3 4(y +…

A:

Q: Find the exact length of the curve. y = In(sec x), 0s x s a/3

A: This question is based on application of Derivative.

Q: The curve y = ax? + bx +c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: Explanation of the answer is as follows

Q: Find dy/dx and d²y/dx². x = 2 + 3, y = t2 + 3t dx d?y dx2 For which values of t is the curve concave…

A:

Q: 10. For x(t)= t² +t,y(t)= e³' find the values oft where the curve is concave down.

A:

Q: Determine d^2 y/ dx2 for the curve: y = 8x^3/2 + e^2x .

A: Given,             y = 8x32 + e2xNow,         y = 8x32 + e2xDifferentiating on both…

Q: Find the length of the curve y=x^4 for 0 &lt;_x &lt;_1 (a) 0.8 (b) 1.0 (c) 1.2 (d) 1.4 (e) 1.6

A:

Q: Find dy/dx and d²y/dx2. x = et, y = te-t dy dx d²y dx2 For which values of t is the curve concave…

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.