3. Quadrature: (a) Use two point Gauss-Legendre quadrature to approximate [²*cos(x²) dr. (b) How many evenly-spaced subintervals do you need for the composite Simpson's method to I dr approximate to within 10-4? 1+x b-a b-a (c) Let h = and derive a quadrature rule ·['₁ f(x) dr h (w₁f(a) + was (a + b = ª) + waf(b) 4 with as high a degree of exactness as you can find. 12 (d) Use your method for part (c) to approximate dr.
3. Quadrature: (a) Use two point Gauss-Legendre quadrature to approximate [²*cos(x²) dr. (b) How many evenly-spaced subintervals do you need for the composite Simpson's method to I dr approximate to within 10-4? 1+x b-a b-a (c) Let h = and derive a quadrature rule ·['₁ f(x) dr h (w₁f(a) + was (a + b = ª) + waf(b) 4 with as high a degree of exactness as you can find. 12 (d) Use your method for part (c) to approximate dr.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.1: Parabolas
Problem 33E
Related questions
Question
![3. Quadrature:
(a) Use two point Gauss-Legendre quadrature to approximate
So
cos(x²) dr.
(b) How many evenly-spaced subintervals do you need for the composite Simpson's method to
10
approximate
x dr
6.⁰
to within 10-4?
1 + x
(c) Let h =
b-a
4
and derive a quadrature rule
• S" S(x) de 2 h (w₁5 (a) + w₂s (a + b = ") + w₁S (b)
4
with as high a degree of exactness as you can find.
(d) Use your method for part (c) to approximate
S²²
[1²
7.4
dr.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff044e349-6d29-4222-b108-8ff4f3301c69%2Fc23397ca-8e89-44f1-b420-a007835528e7%2Fedkd97e_processed.png&w=3840&q=75)
Transcribed Image Text:3. Quadrature:
(a) Use two point Gauss-Legendre quadrature to approximate
So
cos(x²) dr.
(b) How many evenly-spaced subintervals do you need for the composite Simpson's method to
10
approximate
x dr
6.⁰
to within 10-4?
1 + x
(c) Let h =
b-a
4
and derive a quadrature rule
• S" S(x) de 2 h (w₁5 (a) + w₂s (a + b = ") + w₁S (b)
4
with as high a degree of exactness as you can find.
(d) Use your method for part (c) to approximate
S²²
[1²
7.4
dr.
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