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1 The integral ¹8√1 - 16x²dæ 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 cos² x = (1 + cos2x). Enter the value of the integral: b) Find the Maclaurin Series expansion of the integrand as far as terms in xº. Give the coefficient of 4 in your expansion:

1 The integral ¹8√1 - 16x²dæ 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 cos² x = (1 + cos2x). Enter the value of the integral: b) Find the Maclaurin Series expansion of the integrand as far as terms in xº. Give the coefficient of 4 in your expansion:

Advanced Engineering Mathematics
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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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:
Transcribed Image Text: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:
1 The integral f 8/1 – 16x?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 0 and the identity cos? x = (1+ cos 2). Enter the value of the integral: b) Find the Maclaurin Series expansion of the integrand as far as terms in x°. Give the coefficient of x in your expansion:
Transcribed Image Text:1 The integral f 8/1 – 16x?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 0 and the identity cos? x = (1+ cos 2). Enter the value of the integral: b) Find the Maclaurin Series expansion of the integrand as far as terms in x°. Give the coefficient of x in your expansion:
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