16) Approximate ,xer'dx Using Gauss-Legendre 3 points formula G3(f)

Q: Find the solution to the differential equotion that Sotisies the quen inital condiion

A: The differential equation with initial condition is given as

Q: Choose among the following suitable to define the given S(e + +) arctan{ dx O By parts, the red part…

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

Q: Find dy Sinx

A: See the details solution in below

Q: 4 In estimating | cos(3x)dx using Trapezoidal - 1 and Simpson's rule with n = 6, we can estimate the…

A: Error bound of Trapezoidal rule and Simpson rule for integrating f(x)dx in [a,b] is, ET…

Q: tan zeecz coS z

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: 10 Use aepropriate substitution Ond then a trigonometric oubtitution to evaleiate the integial. dx…

A: This question can be solved using the concept of integration by substitution.

Q: Use Taylor’s formula to find a quadratic approximation of ƒ(x, y) = cos x cos y at the origin.…

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Q: Find the length of the hyperbolic function y = cosh x from (0,1) to (8, cosh 8)

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Q: In estimating cos(3x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the error 1…

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Q: 3 In estimating | cos(5x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the…

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Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

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Q: 2 9) -sinh? -cosh -dz

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Q: Find the theoretical error bound in approximating SN" sin(x?) dx using Boole's Rule.

A: The theoretical error bound in approximating the integral∫0πsinx2dx using Boole's rule is shown…

Q: 2. Write closed Newton-Cotes formula with error for n=1, 2, 3 and then solve integral S* sin(x) dx…

A: The Newton cotes formulas are closed when the endpoint of the closed interval is used as a node. The…

Q: use the Mean value Theorem to establish Isine-siny </2-y) Ve,yER

A: We will prove the inequality as following.

Q: 4 1 -dx using the midpoint rule with three subdivisions to four decimal places. In(x) Approximate…

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Q: Calculate the left rectangle approximation of 3x- dx using five subintervals.

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Q: Use the trapezoidal rule withn= 4 to approximate %3D cos(x) COS

A: Given: n=4 and ∫15cos(x)xdxwe know that trapezoidal rule for approximating ∫abf(x)dxis given…

Q: In estimating cos(3x)dx using Trapezoidal and Simpson's rule with n = 4, we can estimate the error…

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Q: Flnd * |(sin 5x cos 3x + cos 5x sin 3x) dx cos 8x cos 3x + 3 cos5x – + c 8 + c Option 3 Option 2 cos…

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Q: In estimating cos(5x)dx using Trapezoidal and Simpson's rule with n = 4, we can estimate the error…

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Q: 4. Find the length of the arc of f(x) = ÷ (1+ x²)ē between x = 0 and x = 3. %3!

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Q: In estimating L cos (5x) dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the…

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Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -π to x = π.…

A: Consider the given function y=4cos0.5x

Q: Ni cos(2?)a. Cos | x dx

A:

Q: Use the trapezoidal rule withn = 5 to approximate 4 cos(x) -dx

A: To approximate : ∫14cosxxdx using Trapezoidal rule with n=5

Q: 2. An explosion is recorded by two microphones that are 2 miles apart. Microphone M, received the…

A:

Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: From 0-2 sin(x^2) dx using trapezoidal rule with n=4 as well as midpoint rule with n=4

A: Trapezoidal rule=∫02sin2(x)......(1)As we know that accoding to trapezoidal rule…

Q: integral from -1 to 1 of arccos (y) dy

A:

Q: In estimating | cos(3x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the error…

A: We have to find the error in trapezoidal and Simpson rule .

Q: integral of (e^2x)(sin3x) using u=e^2x

A: Given, ∫e2xsin3xdx    We have to find the integral

Q: Bring out the importance of Frii's formula.

A: Answer: For the given data

Q: What is the amount of the rotating body formed by rotating the region bounded by the y = cos x…

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

Q: In estimating cos(5x)dx using Trapezoidal and Simpson's rule with n = 6, we can estimate the error 1…

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

Q: 1. Use Fermat's principle to find the path followed by a light ray if the index of refraction is…

A:

Q: use a geometry formula to find the exact value of the definite integral.  5 dx on interval[-2,6]

A: Question is to find the exact value of the definite integral 5dx in the interval [-2 , 6 ]It is…

Q: Use Trapezoidal rule with 5 subintervals and 8 subintervals to find an approximation of x3V-2x4 +…

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Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -pai to x =…

A: given

Q: What are the new limits of integration if apply the substitution u = 4x + t to the integral / sin…

A: We have to change the limit.

Q: 2 = sin5t constitute a fundamenta L

A: Y1=cos5t and y2=sin5t  do not a fundamental set of solutions of differential equations y"+16y=0

Q: The actual error of the approximation of I = x² sin (x³) dx using composite Simpson's rule with n=4…

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Q: The approximation of 1 = f*cos(x³ - dx using composite Simpson's rule with n= 3 is:

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Q: Use the composite Simpson's rule with step length h=0.5 to determine 1= [ (2x - - 3x2 + 4x – 1)dx,

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Q: In estimating : cos(4x)dx using Trapezoidal and Simpson's rule with n = 4, we can estimate the error…

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Q: Evaluate the double integral. 5 25- х2 dy dx Jo

A: First, integrate with respect to y

Q: In estimating | cos(4x)dx using Trapezoidal 1 and Simpson's rule with n = 6, we can estimate the…

A:

Q: Compute integral x^2cos(x^3+3) dx

A: Given : ∫x2cosx3 + 3dx