Evaluate the following integral: - 4x + 2r°) dx (a) Boole's Rule (b) Two-Point Gaussian Quadratüre (cThree Pdint Gaussien Quadrature

Q: Lagrange's Theorem If a function f(x) is continuous in the closed interval [a, b] and is…

A: Proof of Lagrange's theorem.

Q: 3 Evaluate the integral de using the two-point Gaussian quadrature rule O -|4 1035 N/N N/W 끔

A: We have to evaluate the integral ∫−3311+x4dx by using two-point Gaussian quadrature rule. Here,…

Q: ☺ cosh"z= Loy {2+/2

A:

Q: The vertical distance covered by a rocket from 8 to 30 seconds is given by 30 140000 x = 2000 In…

A:

Q: Consider the integral dx, (x² + a²)³/2 where a is a positive real number.

A:

Q: a) Given an integral sin (2x-) dr. T-I [." Evaluate the above integral using 3-point Gaussian…

A: 3-point Gaussian quadrature rule: The following integration can be approximated by ∫-11f(x) dx ≈59…

Q: a) Use the definition of the hyperbolic functions to prove that 2cosh?(x)–1=cosh(2x). 1%3D

A:

Q: Fineling the derivative of trigonometric %3D

A: Given:  f(x)=ln(2+x )

Q: a) sketch the curves of f(x) and g(x) in the same plane b) calculate the area covered by the two…

A:

Q: (1 if 0 1

A: The given function is,f(x)=1 if 0<x<10, if x>1

Q: (a) Show that v.ve =p²o, where v- S+ denote the Laplacian operator

A: We will prove the following result.

Q: 6a) Let A be the parabolic arc defined by the equation y = 8x – x´ over the domain interval [0, 8].…

A: (a) Consider the given function. y=8x-x2 Now, draw the above function by using the calculator.

Q: Evaluate the integral S de using the two-point Gaussian quadrature rule

A: For the integral I=∫abf(x)dx, the Gaussian quadrature 2-point formula is,I=b-a2w1fm1+w2fx2where…

Q: Integrate by Gaussian quadrature (n=3). dx Ji 1+x*

A:

Q: 4) Activity 5: Check for Understanding ASSIGNMENT #5. Evaluate the definite integral using the first…

A:

Q: Use two -point gaussian square to approximate the following double integral:

A:

Q: ) Find the derivetine of the fnchiog h(x) = I sinhex-7x 4

A: h(x)=74sinh(2x)-7x2Differentiate w.r.t…

Q: Evaluate the definite integral 2x dx in two -3 different ways: (2a) as a net area. Sketch the…

A: From the above graph, the net area is area from 0 to 1 = 1 area from -3 to 0 is -9. So net area =…

Q: method determine ? unique üOl zy Use Seperation of Variables to to the Laplace quation for x6l0.7)…

A:

Q: 3) Using the Fundamental Theorem of Calculus (FTC), find the exact values of the following definite…

A:

Q: Use the symmetry method to evaluate the following integrals.

A:

Q: Other Applications of Newton's Methood a) Use Newton's Method to determine the critical values of…

A: (a) The critical points are located at x values for which y=g(x)=ex+x2=0.If there exists any root…

Q: Solve for y in terms of x for the foltowing

A: e(ln2)y=12lne(ln2)y=ln12yln2=-ln2y=-1

Q: Prove this equa tion analy tic fcz)z Ln /21+iargz Ln 12|+iarg

A: Equation proving in analytical way