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Let f(x) = √ sin t dt. t This is called the sine integral and is denoted Si(z). (a) Replace sin(t) by your Taylor series from the previous problem (written as an expanded sum), and evaluate the integral term by term. (b) Use the first four nonzero terms of the series to approximate Si(1). Compare this to the value you get by using your calculator or Desmos to calculate Si(1) from the definition.

Let f(x) = √ sin t dt. t This is called the sine integral and is denoted Si(z). (a) Replace sin(t) by your Taylor series from the previous problem (written as an expanded sum), and evaluate the integral term by term. (b) Use the first four nonzero terms of the series to approximate Si(1). Compare this to the value you get by using your calculator or Desmos to calculate Si(1) from the definition.

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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7. Let f(x) = √ s sin t dt. This is called the sine integral and is denoted Si(z). (a) Replace sin(t) by your Taylor series from the previous problem (written as an expanded sum), and evaluate the integral term by term. (b) Use the first four nonzero terms of the series to approximate Si(1). Compare this to the value you get by using your calculator or Desmos to calculate Si(1) from the definition.
Transcribed Image Text:7. Let f(x) = √ s sin t dt. This is called the sine integral and is denoted Si(z). (a) Replace sin(t) by your Taylor series from the previous problem (written as an expanded sum), and evaluate the integral term by term. (b) Use the first four nonzero terms of the series to approximate Si(1). Compare this to the value you get by using your calculator or Desmos to calculate Si(1) from the definition.
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