The integral 5√1-92²da is to be evaluated directly and using a series approximation. (Give all your answers rounded to 3 significant figures.) a) Evaluate the integral exactly, using a substitution in the form ax = sin and the identity cos²x = (1 + cos2x). Enter the value of the integral: b) Find the Maclaurin Series expansion of the integrand as far as terms in Ⓡ. Give the coefficient of 4 in your expansion: C) Integrate the terms of your expansion and evaluate to get an approximate value for the integral. Enter the value of the integral: d) Give the percentage error in your approximation, i.e. calculate 100x (approx answer - exact answer)/(exact answer). Enter the percentage error: %.
The integral 5√1-92²da is to be evaluated directly and using a series approximation. (Give all your answers rounded to 3 significant figures.) a) Evaluate the integral exactly, using a substitution in the form ax = sin and the identity cos²x = (1 + cos2x). Enter the value of the integral: b) Find the Maclaurin Series expansion of the integrand as far as terms in Ⓡ. Give the coefficient of 4 in your expansion: C) Integrate the terms of your expansion and evaluate to get an approximate value for the integral. Enter the value of the integral: d) Give the percentage error in your approximation, i.e. calculate 100x (approx answer - exact answer)/(exact answer). Enter the percentage error: %.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The integral 3 5√/1 - 9x² dx is to be evaluated directly and using a series approximation. (Give all your answers rounded to 3 significant figures.)
a)
Evaluate the integral exactly, using a substitution in the form ax = sin and the identity cos²x = (1 + cos2x).
Enter the value of the integral:
b)
Find the Maclaurin Series expansion of the integrand as far as terms in 6. Give the coefficient of 4 in your expansion:
c)
Integrate the terms of your expansion and evaluate to get an approximate value for the integral.
Enter the value of the integral:
d)
Give the percentage error in your approximation, i.e. calculate
100x (approx answer - exact answer)/(exact answer).
Enter the percentage error:
%.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F19f03189-dea3-4775-a3d5-7a4c15c68ea9%2Fc1f8f59b-9d69-449f-8d80-b9f59ff99c50%2Fq0begjq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The integral 3 5√/1 - 9x² dx is to be evaluated directly and using a series approximation. (Give all your answers rounded to 3 significant figures.)
a)
Evaluate the integral exactly, using a substitution in the form ax = sin and the identity cos²x = (1 + cos2x).
Enter the value of the integral:
b)
Find the Maclaurin Series expansion of the integrand as far as terms in 6. Give the coefficient of 4 in your expansion:
c)
Integrate the terms of your expansion and evaluate to get an approximate value for the integral.
Enter the value of the integral:
d)
Give the percentage error in your approximation, i.e. calculate
100x (approx answer - exact answer)/(exact answer).
Enter the percentage error:
%.
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