HW7_4 We wish to find the result of sin(ex - 2) dx However, this function is difficult to integrate. Hence, instead of calculating ¹6 sin(ex - 2) dx we will estimate its value by computing the integral of the interpolating polynomial fitted through the following data points which are the actual values of f(x) = sin(ex - 2). This is a much easier task as polynomials are easy to integrate and it provides a good estimate if the two functions are look close to each other when plotted (areas under the curves are also similar) X 0 0.4 0.8 1.2 y -0.8415 -0.4866 0.2236 0.9687 1.6 0.1874 Accordingly, carry out the following tasks (all plots are to be produced on the same figure): a) Plot the above data points using discrete point plotting. b) Plot the function f(x) = sin(e* - -2). c) Use polyfit to do polynomial interpolation for the above data. Plot the interpolating polynomial, using polyval. d) At this point, run your code to produce the plotting results. Do f(x) and the interpolating polynomial follow each other closely? Do you believe that our plan will produce a good estimate? Record your opinion with a print statement. e) Integrate the polynomial by hand, then compute the value of the exact integral using PYTHON. Print the final result using print.
HW7_4 We wish to find the result of sin(ex - 2) dx However, this function is difficult to integrate. Hence, instead of calculating ¹6 sin(ex - 2) dx we will estimate its value by computing the integral of the interpolating polynomial fitted through the following data points which are the actual values of f(x) = sin(ex - 2). This is a much easier task as polynomials are easy to integrate and it provides a good estimate if the two functions are look close to each other when plotted (areas under the curves are also similar) X 0 0.4 0.8 1.2 y -0.8415 -0.4866 0.2236 0.9687 1.6 0.1874 Accordingly, carry out the following tasks (all plots are to be produced on the same figure): a) Plot the above data points using discrete point plotting. b) Plot the function f(x) = sin(e* - -2). c) Use polyfit to do polynomial interpolation for the above data. Plot the interpolating polynomial, using polyval. d) At this point, run your code to produce the plotting results. Do f(x) and the interpolating polynomial follow each other closely? Do you believe that our plan will produce a good estimate? Record your opinion with a print statement. e) Integrate the polynomial by hand, then compute the value of the exact integral using PYTHON. Print the final result using print.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:HW7_4 We wish to find the result of sin(x - 2) dx
1.6
However, this function is difficult to integrate. Hence, instead of calculating ¹6 sin(ex − 2) dx we will
estimate its value by computing the integral of the interpolating polynomial fitted through the following data
points which are the actual values of f(x) = sin(e* — 2). This is a much easier task as polynomials are easy to
integrate and it provides a good estimate if the two functions are look close to each other when plotted (areas
under the curves are also similar)
X 0
y
0.4
0.8
1.2
-0.8415 -0.4866 | 0.2236 0.9687
1.6
0.1874
Accordingly, carry out the following tasks (all plots are to be produced on the same figure):
a) Plot the above data points using discrete point plotting.
b) Plot the function f(x) = sin(e* — 2).
c) Use polyfit to do polynomial interpolation for the above data. Plot the interpolating polynomial,
using polyval.
d)
At this point, run your code to produce the plotting results. Do f(x) and the interpolating polynomial
follow each other closely? Do you believe that our plan will produce a good estimate? Record your
opinion with a print statement.
e) Integrate the polynomial by hand, then compute the value of the exact integral using PYTHON. Print the
final result using print.
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