1 xp: J 3x/x² – 81 A farene () -e °rene () + -Arcsec 9 1 Arcsec В. 27 9 1 C. Arcsin (5) Are 1 뉴Arcsin () +c :Arc sin c D. 27 9.

Q: Evaluate 112² (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32)

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Q: The arc length of the curve r= cos 30 with 0<0<nis попе J V-9(sin 30)² + (cos 30)² d0 I (sin 30)² +…

A: In this question we have to find the arc length of the curve.

Q: Evaluate (2x – y) dx + (x + 3y) dy. C: arc on y = x312 from (0, 0) to (4, 8)

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Q: Show that the volume of solid formed by revolving one loop of the curve r2 = a? cos20 about the line…

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Q: Find the arc length (s) of the curve 7(t) = (4 cos( – 4t), 2/5 cos( – 4t), 6 sin( – 4t)) for 0 <t <…

A: Given that  The curve is  To find the arc length of the curve

Q: Evaluate | (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 32)

A: Follow the procedure given below.

Q: 2 ind the arc length for f(x) = 6-2 x² over the interval [0, 2].

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Q: Evaluate [12x. (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 32)

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Q: (b) y = e=* + + In(3z + 1) (c) y = (cos z)° + sin(2*) (d) y = #° arcsin(2*)

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Q: Evaluate 112x C: arc on y = x5/2 from (0, 0) to (4, 32) (2x - y) dx + (x + 3y) dy.

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Q: Find the arc length of C = 1.5 - 2.1 First find and simplify√1 + y2² Now integrate to find arc…

A: Hint: Here in order to solve we will use formula of arc length, L =∫ab1+(y')2dx, where a≤x≤b.

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 8)

A: Here we have to evaluate        ∫c (2x-y)dx+(x+3y)dy

Q: Consider a particle moving along a path C given by r(t) = v3ti+ = V3ti sin (t)j + cos (t)k Find the…

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Q: Evaluate S (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32)

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Q: -1 Suppose y = sin ¹x. Then y arcsin 1 Oy= sin a Or = siny Or=

A: Given that:- y= sin--1x. Then  Topic:- inverse trignometry

Q: Use trapezoidal with 3 level Romberg ( k=3) to evaluate 1 Пх - Пх* cos dx 4

A: The complete solutions are given below

Q: |3| 7/7 2) Find the arc length of y = ln (sec x) from x = 0 to r 11

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Q: du nd az and " if z = 5 tan-'(x)and x = e" + In(v) at tl-

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Q: 33. (a) Show that the total arc length of the ellipse x = 2 cos t, y = sint (0 <t< 27) is given by…

A: Given: x=2cost  , y=sint   0≤t≤2π To show : The length of total arc is  4∫0π21+3sin2tdt

Q: Evaluate (2x – y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 32)

A: This is a problem related to vector calculus. Based on green's theorem we will solve the integral.

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x12 from (0, 0) to (4, 8) 528/5

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Q: 3. Arctany dy

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Q: Consider the parametric curve: x = ln (8t) y = 5t³ Which integral gives the arc length of the curve…

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Q: Find the arclength of the curve x 5 cos(3t), y = 5 sin(3t) with 0 <t< 6

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Q: 7. Find the arc length of each curve (integrate by hand) a) x = -8y– 3 on [– 2,6] b) y = , 3 on…

A: Here we have to find the arc length of the given curves.

Q: I. Find dy/dx in the following: 3. Y= tan (1+sinx)

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Q: 2. What is the arc length of the polar curve r = 1- sin 0 for 0 <0< <5? 2 (a) 2(v2 – 1) 2 - V2 2/2…

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Q: Compute for the arcsinx dx . Which of the following is not an antiderivative of the function f(0) =…

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Q: Estimate 1 7 cos(x2) dx 0 using the Trapezoidal Rule and the Midpoint Rule, each with n = 4. (Round…

A: I=∫017 cos (x2) dx             f(x)=7 cos (x2)b=1, a=0, n=4h=b-an=14=0.25aThe Trapezoidal…

Q: What is the arc length of the curve x = (1/2)y2 - (1/4)ln y from y = 1 to y = e?

A: Here, we have given x is a function of y. So, we will use the following formula for finding the arc…

Q: Find the arc length of the curve x = a cos3θ, y=a sin3θ in [0,2π].

A: The arc length formula for the parametric curve on the interval [a,b] is given by: Hence compute…

Q: 2. Find the arc length of (x+5 y= over the closed interval [-1,4] .

A: Given curve is

Q: Evaluate Ic (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32) X

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Q: 1. Find the arclength of y= (4 -x3,3/2 from x = 1 to x = 8.

A: The arclength of given equation

Q: Find the arc length of the graph of y = In(cosx) from x = 0 to x =- 4 O A. In(v2) B. In(2) C. 0,75 O…

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Q: 4.2. Calculate the arc length of the cardioid given by r = a(1 – cos 0) -

A: The cardioid is symmetrical in nature and ranges from θ=0 to θ=π as a half figure. We can also…

Q: 7. Find the arc length of the following plane curve: x = e' (sint + cos t), y = e' (cost – sin t),…

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Q: The arc length of the curve r= cos 30 with 0<0 < is T V(sin 30)² + (cos 30)² do 0. o" V-9(sin 30)² +…

A: Given that: r=cos3θand  0≤θ≤π

Q: II. Draw a sketch of the given arc C and evaluate Sc [(x² − 2y)dx + (2x + y²)dy]. → 1. C is part of…

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Q: Evaluate (2х — у) dx + (х + Зу) dy. C: arc on y = x72 from (0, 0) to (4, 32) 512/7

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Q: Evaluate (2x – y) dx + (x + 3y) dy. C: arc on y = x>12 from (0, 0) to (4, 32)

A: Solution is given below..

Q: Evaluate / (2x – y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32) 11760/7 X

A: Explanation of the answer is as follows

Q: find the arca of he shaded regon. Ue a calcularor apter xmng up tde integal. cos 20

A: Let r1=cos2θ and r2=2cosθ. We know that a polar coordinate is represented as r, θ, where r=x2+y2 and…

Q: b) y = ln (cos x) 0 <x<- 3

A: Given: y=ln(cosx) in the interval 0≤x≤π3

Q: Find the arc length of the curves x = e-20 (sine + cos0), y = e-20 (sine – cose) over the interval…

A: Definition used -                    Length of the curve…

Q: Show that the total arc length of the ellipse x = 2 cos t, y = sin t (0 <1< 27) is given by /2 4 V1…

A: Arc length is the total distance of the boundary of any curve. If the equation of ellipse is in…

Q: Consider the parametric curve: X y = ln(-t) Which integral gives the arc length of the curve over…

A: We have to find the length of curve.

Q: The arc length of the curve r= cos 30 with 0<0<T is J V (sin 30)² + (cos 30)² d0 T" V-9(sin 30)² +…

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Q: The area of the rotational surface resulting from rotating the arc of the curve x=cos^3 t, y=sin^3 t…

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