sin x dx accurately to four decimal places. (a) Use the Maclaurin series for sin (u), substituting u=x², to write a power series for sin (x²). (b) Integrate this power series term-by-term to write a new power series for the integral sin x² dx. (c) Now evaluate the power series resulting from your integration in part (b) from x=0 to x=1, to obtain a series of constant terms. (d) Find a decimal approximation for the value of this resulting series of constant terms that is accurate to 4 decimal places. As part of your answer, you should cite a theorem justifying your claim to know that your approximation is as accurate as desired.
sin x dx accurately to four decimal places. (a) Use the Maclaurin series for sin (u), substituting u=x², to write a power series for sin (x²). (b) Integrate this power series term-by-term to write a new power series for the integral sin x² dx. (c) Now evaluate the power series resulting from your integration in part (b) from x=0 to x=1, to obtain a series of constant terms. (d) Find a decimal approximation for the value of this resulting series of constant terms that is accurate to 4 decimal places. As part of your answer, you should cite a theorem justifying your claim to know that your approximation is as accurate as desired.
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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Question
Use a power series approach, to following the steps outlined below, to approximate the value of:
Transcribed Image Text:sin x² dx accurately to four decimal places.
0
(a) Use the Maclaurin series for sin(u), substituting u=x², o write a power series for sin (x²).
(b) Integrate this power series term-by-term to write a new power series for the integral [ sin(x²) dx.
(c) Now evaluate the power series resulting from your integration in part (b) from x=0 to x = 1,
to obtain a series of constant terms.
(d) Find a decimal approximation for the value of this resulting series of constant terms that is accurate to
4 decimal places. As part of your answer, you should cite a theorem justifying your claim to know that
your approximation is as accurate as desired.
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