A string of length 27 m has both ends free. Initially the string has a vertical displacement of the shape 3+4 cos(2x) with velocity 5 cos r m/s, where a is the length measured from one end. Define and solve the boundary value problem for the vertical displacement of this string with respect to time and position.

Q: Evaluate the integral (2x+3y) dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

A: To Evaluate: I=∫C(2x+3y)dx+(6x-y)dy along the parabolic arc y=x2 from (0,0) to (1,1).

Q: 1- Use trapezium's Rule with n = 4 to approximate the integral Vx dx

A: We have to use formula of Trapezoid Rule.

Q: 6.Solve the following boundary value probletn: at2 U(0, t) ='U(x, t) == 0 U(x,0} = sin x + 2sin 2x…

A: To Solve: The boundary Value Problem : ∂2U∂x2 = ∂2U∂t2U(0,t) = 0U(π,t)=0U(x,0)= sin x+2 sin…

Q: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: Use Simpson's rule with interval h = 1 to determine the approximate value of 6 V(1 + x³)dx. Give…

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Q: # 1) If V is the volume of a cube with edge length x and the cube expands as time passes, find dV/dt…

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Q: Evaluate the integral (12x + 12y)dx + (9x - y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

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Q: The arc-length of the curve y= Vcos(21) dt , for 0<x<= is given by which of the following integrals?…

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

Q: Evaluate the integral (8x + 12y)dx + (9x – y)dy along the parabolic (8x +12y)dx + (9x – y)dy along…

A: We need to evaluate the integral ∫C(8x+12ydx+(9x-y)dy along the parabolic arc y=x2. from (0,0) to…

Q: 4. Find the volume of the solid generated by the curve f(x)=4-cos.x revolved 360° about the x- axis…

A: Please check the region, given region is not bounded, we consider the region bounded by curve, x=0,…

Q: 3. Solve the integral by two grid in the y-direction and four grid in the x-direction with…

A: Solve the integral by two grids in the y axis and four grids in the x axis with Trapezoidal rule:…

Q: Consider a rod of length meters with density 8(x)=(2- cos x) kg/m over the interval 0<x<5.

A: Given that The length of rod is π2 and the density of the rod is δ(x)=2-cos(x)  with 0≤x≤π2 To find…

Q: Use Secant method to to approximate the solution of f(r) = z+ cos z =0 accurate to within 10-3,…

A: The secant method is used to calculate the root of the function. The formula for the secant method…

Q: The forces of the human gastrocnemius tendon during traction and during recoil can be approximated…

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Q: (1,2) (b) Set up a definite integral that is equal to the arc length of the portion of the circle…

A: Note:- As per your request i am solving here question no. 3 part B only.

Q: Evaluate the integral / (10x + 15y)dx + (18x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: 2 1 To evaluate the improper integral . v3+ 125 will tend to infinity). What is the minimum value of…

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Q: Find the approximation of the integral. 1= [e*dx Using Romberg's rule derived from Trapezoidal rule…

A: Given integral I=∫01e-x2dx Here we use Romberg's rule derived from Trapezoidal rule for 1,2,4,8…

Q: Find the solution of the integration using trapezoids and Simpson's 1/3 rule and compare the…

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Q: Find the temperature u(x, t) in a rod of length L, if the initial temperature is f (x) = 100 sin 6nx…

A: Given function is, fx=100sin6πx at x=0 and x=L Now, we know that, ∂2t∂x2+qgk=1α·∂t∂z....(1)

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 | (- 2* + 20z – 96z?…

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Q: au Show that the local truncation error at the pint (ih,jh) of the Crank-Nikolson approximation to…

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Q: The radius of a sphere is measured and found to be 3 ft. with a maximum error of 0.1 in. Find the…

A: The solution of the problem is given in the next step.

Q: Evaluate the integral (8x +12y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

A: Topic:- integration

Q: Find the temperature u(x, t) in a rod of length L, if the initial temperature is f (x) = 100 sin 6nx…

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Q: Evaluate the integral / (8x + 3y)dx + (18x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A: Explanation of the solution is given below....

Q: Evaluate the integral (12x + 6y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: Verify the given linear approximation at a=0 . Thendetermine the values of  x for which the linear…

A: Concept Used: Linear approximation of f(x) at x = a is

Q: The base radius and height of a right circular cone are measured as 10cm and 25cm, respectively,…

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Q: A particle moves along a line with avelocity given by v(t) = 5 sin ∏t, starting with an initial…

A: Given equation of the position - s(t) = ∫02v(t) dt              ..................(1)given that,v(t)…

Q: Find the temperature u(x, t) in a rod of length L, if the initial temperature is f(x) = 100 sin 6Tx…

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Q: Set up an integral that (if solved) would give the arc-length of the following curve on the given…

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Q: The suitable substitution to evaluate the integral (V cot (2x) dx is sin (2x) Ou3tan(2x) none Ou=…

A: To find The suitable substitution to evaluate the integral.

Q: 2.a) Apply the Trapezoid and corrected trapezoid rule, with h = 1, to approximate the integral 1 dx…

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Q: Determine the avarage Valve of + he Aunction fex)=Cas(z)-Sin Cx/2) PA L-2, by using The meen vaelve…

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Q: Approximate the integral S" x² sin x dx by Trapezoidal rule with n = 4. O Find the minimum n…

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Q: Evaluate the line integral (4х + 5у)dx + (За — 6у)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: aluate the iterated double integral. 1 cos(y) /5 + cos² (y) dydx Saresin (2)

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Q: Find the work done in stretching a spring of natural length 8 cm, from 10 cm to 13 cm. Assume a…

A: Given information:- Find the work done in stretching a spring of natural length 8 cm, from 10 cm to…

Q: 1, fund warginal cictribution for h(x) for 2. Fud condhtimal pdf4 t) . Estaati yi/ a) V. Estuate…

A: As per the guideline, 3 subparts can be answered. please repost the remaining subpart. thank you.

Q: Evaluate the integral | (2x + 9y)dx + (21x – y)dy along the parabolic arc y = x from (0,0) to (1,…

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Q: Compute the defined integral So [1+ e* sin(4x)] dx using the trapezoidal method with two segments.…

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Q: Evaluate the integral / (8x + 18y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A: We have to find value of given Integral along given Curve.

Q: A sphere of radius 2 cm contains a volume charge density Pv given by py = 4 cos“0 [C/m³]. Find the…

A: Given: Radius of the sphere=3 cm Charge density, ρv=4 cos2θ C/m3

Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to…

A: For the arc y = x2 and the range of x from 0 to 1. So, dy = 2x dx. Now,…

Q: . The work required to move a mass m "infinitely far" from a planet of radius R and mass M is given…

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Q: Evaluate the integral (12x + 12y)dx + (9x-y)dy along the parabolic arc y = x from (0,0) to (1,1).…

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Q: Solve the integral by two grid in the y-direction and four grid in the x-direction with Trapezoidal…

A: The given integral is: ∫45∫23xcosydydx Here  x0=4, x1=5y0=2, y1=3fx,y=xcosy By Trapezoidal rule,…