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so , here we get degre is 2 ..because for putting x^3 in equation ..left and right not give same result....
Given the following quadrature formula: (x)dx = c0) + f(a) Find a 4 and 2 so...
4. Consider the quadrature rule +s0) 2 (F'0) +35() + 3fj f (x)dx Determine the degree of precision of this rule, that is, find the highest degree of polynomial for which the above rule is exact. (10 marks) OC 4. Consider the quadrature rule +s0) 2 (F'0) +35() + 3fj f (x)dx Determine the degree of precision of this rule, that is, find the highest degree of polynomial for which the above rule is exact. (10 marks) OC
3. (1 point) This is 2-point Gaussian Quadrature for any f(x) dx. The weights and the nodes do not change when we integrate a new function. So...does it work? Does this actually lead to a method that is good for intergating functions in general? Use 2-point Gaussian quadrature to approximate the following integral: I e-ra da. -1 The exact value of this integral rounded to 2 decimal places is 1.49. Show your work when computing the approximation. Report the answer...
If Si f(x)da = 12 and so f(x) = 2.8, find si f(x)dx. Question 2 1 pts Let f(x)dx = 6, S. 8(x)dx = -4, S g(x)da = 12, g(x)dx = 9 Use these values to evaluate the given definite integral: (+1) da
Use the inner product <f,g>=∫10f(x)g(x)dx in the vector space C0[0,1] to find <f,g>, ||f||, ||g||, and the angle θf,g between f(x) and g(x) for f(x)=5x2−9 and g(x)=−9x+2.
this is numerical analysis. Please do all the questions 3. (a) Consider the quadrature rule path ( * s(a)dx = Af (a – 1) + Bf(a) + Cf(a+h). Find A, B, C which maximize the degree of precision. Hint: First derive the rule for a = 0 and then use a change of variable. (b) State this degree of precision and verify it is not any higher. (c) Suppase g is a function whose 3rd divided differences are all the...
(a) Find the degree 1 interpolating P(x) through the points (a, f(a)) and (b, f(b)) (b) Develop the following formula by using the interpolating polynomial P1 (x), (c) Find the degree of precision of the approximation, T1 (f) = f(1) + f(-1), for f(r)dr. (a) Find the degree 1 interpolating P(x) through the points (a, f(a)) and (b, f(b)) (b) Develop the following formula by using the interpolating polynomial P1 (x), (c) Find the degree of precision of the approximation,...
3. |(6x2/3 + 2 cos x – 5) dx 4. Find f(x) given that f'(x) = 5x4 – 3x2 + 2 and f(1) = 4.
5. Find which of the following quadrature formulas are of the interpolatory type. Show your analysis. b) x)dx f(-1)+f(). 5. Find which of the following quadrature formulas are of the interpolatory type. Show your analysis. b) x)dx f(-1)+f().
2. E F Given the graph above find the following net area: a. Së f(x) dx b. Së f(x) dx c. Sc2f(x) dx d. Sº if(x) dx e. Sflf (x)]dx f. Si f(x) dx
Problem 1. Consider an integral of the form 1 (f) = f0 /if (x) dx. Show that the one-point Gaussian quadrature rule for integrals of the form Jo VRf (x) dx has the node x1and weight w3 Problem 1. Consider an integral of the form 1 (f) = f0 /if (x) dx. Show that the one-point Gaussian quadrature rule for integrals of the form Jo VRf (x) dx has the node x1and weight w3