6. Consider the following function: and the fact that: f(x)= 2nσ exp 2 20² f(x) dx = 1 answer the following questions (you must submit an excel file with calculations and answers). a. Assuming μ = 0,0² = 1, use the Trapezoidal rule with x=2, 4, x=6 to compute the integral: Sf(x)dx. b. Assuming μ = 0,0² = 1, use Simpson's rules with x=2, 4, x=6 to compute the integral: Sf(x)dx. c. Assuming μ = 0,0² = 1, use Simpson's rule with x=2, x=4, a=6 to compute the integral: Sxf(x)dx.
6. Consider the following function: and the fact that: f(x)= 2nσ exp 2 20² f(x) dx = 1 answer the following questions (you must submit an excel file with calculations and answers). a. Assuming μ = 0,0² = 1, use the Trapezoidal rule with x=2, 4, x=6 to compute the integral: Sf(x)dx. b. Assuming μ = 0,0² = 1, use Simpson's rules with x=2, 4, x=6 to compute the integral: Sf(x)dx. c. Assuming μ = 0,0² = 1, use Simpson's rule with x=2, x=4, a=6 to compute the integral: Sxf(x)dx.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:6. Consider the following function:
and the fact that:
f(x):
=
1
2лσ²
exp
Sof(x) dx = 1
2
answer the following questions (you must submit an excel file with calculations and answers).
a. Assuming μ = 0,0² = 1, use the Trapezoidal rule with #=2, #=4, #=6 to compute the
integral:
Sf(x)dx.
202
b. Assuming μ = 0,0² = 1, use Simpson's rules with n=2, n=4, n=6 to compute the integral:
Sf(x)dx.
c. Assuming μ = 0,0² = 1, use Simpson's rule with #=2, 4, n=6 to compute the integral:
Sxf(x)dx.
(Hint: Don't forget the change of variable).
e. Assuming μ = 0,0² = 1, use Gauss-Hermite quadrature with #=4, #=6 to compute the integral:
Sxf(x) dx.
f. Assuming μ = 0,0² = 1, use Gauss-Hermite quadrature with #=4, #-6 to compute the integral:
Sx²f(x)dx.
g. Assuming μ = 1,0² = 2, use Gauss-Hermite quadrature with #=-4, #=6 to compute the integral:
Sxf(x)dx.
(Hint: Don't forget the change of variable).
h. Assuming μ = 1,0² = 2, use Gauss-Hermite quadrature with =4, #=6 to compute the integral:
(x-μ)² f(x)dx.
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