8- Find the lengthf the Curve are 24xy=x+48 Hem X=2 tox=y Hint The eure Can be written as fettow +2X 24

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: Hw. Find the lengths Ror the fallowing Curvere 2-

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Q: Find the length of the curve x=2t, y=3t, 0≤t≤1

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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: Find the length of the curve: r = 5cos 0 1 2 3 4

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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 length of the curve r = θ2−1 from θ =1 to θ = 2

A: TO FIND THE LENGTH OF THE CURVE r = ∅2-1      from  ∅ =1  to ∅ =2 USING FORMULA ∫abr2 +(drd∅)2   d∅

Q: Find the length of the curve: 7= Scos 4. t2.

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

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Q: 10. Find the length of the curve y = x/2 + 8 on the interval [0, 2]

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Q: 3t? Find the length of the curve x = t, y 2 osts 13. 3 =

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Q: 2 y = In (x-√x²-1), for 1 ≤ x ≤ √/485 (Hint: The length of the curve is (Simplify your answer)

A: Topic:- application of derivatives and integration

Q: 64. Find the length of the curve y = 1 - e",0 SISI.

A: Formula to find the length of the curve helps to find the required length. Formula to find the…

Q: Find the exact length of the curve. x = 2/3t3,  y = t2 − 2,  0 ≤ t ≤ 2

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Q: Find the exact length of the curve y2 = 16(x + 1)3,   0 ≤ x ≤ 3,  y > 0

A: See the attachment

Q: Find the length of the curve. y = 2 – 4x, 1<a< 3 O 54 3V17 O 17 O 2y17

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

A: Given polar curv er=eθ   ; 0≤θ≤2π

Q: 1. Find the length of the curve 9x2 = 4y from (0,0) to (2V3,3) %3D

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Q: Find the length of the following curve. 3 2 y = 2x from x= 0 to x= 6 The length of the curve is

A: To find the length of the curve  y=2x32 from x=0 to x=6

Q: Find the exact length of the curve. x = 4 + 3t2,    y = 1 + 2t3,    0 ≤ t ≤ 3

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Q: Find the exact length of the curve. x = 4 + 3t2,    y = 1 + 2t3,    0 ≤ t ≤

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Q: d the exact length of the curve. y = 1 + 8x3/2, Osxs1

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Q: Find the exact length of the curve. x = 4 + 6t2 y = 6 + 4t3 0 sts 4

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Q: 3 y + 3 Find the length of the curve x = 18 2у on 3sys5.

A: Length of the curveL=∫ds where ds=1+dxdy2dy y is between 3  and 5…

Q: Find the length of the curve. t,0stsV3 The length of the curve x = t°, y= ť on 0sts 3 is (Type an…

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

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Q: Find the exact length of the curve. 1 + 1sys 2 8 4y2

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Q: Find the length of the curve. x=(y - 1) 3/2 from y = 1 to y = 4 O 7 O 10 21 2 O 1

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Q: Q5) Find the length of the curve: r = asin? ,0 0.

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Q: Find the exact length of the curve. X = Vу (у — 3), 16 <y S 25

A: First differentiate wrt y

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

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Q: 11. Find the exact length of the curve x = 1+3t2, y = 4 + 2t3,0 <t <1. page 11

A: Arc length = ∫abdxdt2+dydt2dt

Q: Find the exact length of the curve. y = In(sec(x)), 0<x< 1/4 %3D

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Q: Find the exact length of the curve. 1 + x?)3/2, 0sxs2 y

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Q: Find the length of the curve. x = (v - 1) 3/2 from y = 16 to y = 25 O 4 61 O IK

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Q: Find the length of the curve r(t)=, -2 "< or equal to" 0, "< or equal to" 2.

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Q: 5. Find the length of the curve = = = (1 ²+2) X=- 3 9 0≤ y ≤ 4

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Q: Find the length of the curve. 2ti + etj + e k, 0<tS 4

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Q: Find the length of the curve 24xy = y + 48, Select one: 85/85-8 243 80/10-13/T3 27 O None of these

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Q: The siope of a line tangere to the curve y=fx)at(3 4) 0f iz cists) equais

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Q: 5. Find the length of the curve y = 2(2+ x)², 1<x<8 %3D

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Q: Find the length of the curve Y = 4x^3/2 from x = 0 to x = 5/16

A:

Q: Find the exact length of the curve. 1 1 s x s 3 y 4x

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

Q: Find the length of the curve. 9. r(t) = i-j+ 6t k, 1sts3 %3D 74 3 88 3 O 16 3 O 70 3 92 3

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Q: Find the length of the curve. r(t) 4 it2j3k, 0 st s 1

A: Consider the curve x = 4, y = t2 and z = t3.The derivatives are

Q: Find the exact length of the curve. x =  2 3t3,      y = t2 − 2,      0 ≤ t ≤ 2

A:

Q: 10. Find the length of the curve y = x/2 + 8 on the interval (0, 2]

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.