Question

In previous classes you learned about numerical integration techniques, including Simpson's rule. We want to compare this to using Maclaurin series. An integral that comes up often in statistics is a variation on $\int_0^a e^{-x^2} dx$, which is used to find probabilities for the normal distribution. A) Approximate $\int_0^{0.56} e^{-x^2} dx$ using Simpson's rule with 4 subdivisions. Be sure to maintain at least 5 significant digits in intermediary calculations, or use a calculator to maintain the accuracy. You are welcome to include a screenshot of a calculator in your work rather than typing out the details. B) Approximate $\int_0^{0.56} e^{-x^2} dx$ by using a finding a Taylor series for $e^{-x^2}$, integrating, then evaluating the degree 9 Taylor polynomial. C) Compare each result to the \"actual\" integral obtained from a calculator. Which is more accurate? Which was easier to compute? Upload your work here. You can use Insert->Image to add pictures, or Insert->Attach File to add other files.

          In previous classes you learned about numerical integration techniques, including Simpson's rule. We want to compare this to using Maclaurin series.
An integral that comes up often in statistics is a variation on $\int_0^a e^{-x^2} dx$, which is used to find probabilities for the normal distribution.
A) Approximate $\int_0^{0.56} e^{-x^2} dx$ using Simpson's rule with 4 subdivisions. Be sure to maintain at least 5 significant digits in intermediary calculations, or use a calculator to maintain the accuracy. You are welcome to include a screenshot of a calculator in your work rather than typing out the details.
B) Approximate $\int_0^{0.56} e^{-x^2} dx$ by using a finding a Taylor series for $e^{-x^2}$, integrating, then evaluating the degree 9 Taylor polynomial.
C) Compare each result to the \"actual\" integral obtained from a calculator. Which is more accurate? Which was easier to compute?
Upload your work here. You can use Insert->Image to add pictures, or Insert->Attach File to add other files.

In previous classes you learned about numerical integration techniques, including Simpson's rule. We want to compare this to using Maclaurin series.
An integral that comes up often in statistics is a variation on ∫0^a e^-x^2 dx, which is used to find probabilities for the normal distribution.
A) Approximate ∫0^0.56 e^-x^2 dx using Simpson's rule with 4 subdivisions. Be sure to maintain at least 5 significant digits in intermediary calculations, or use a calculator to maintain the accuracy. You are welcome to include a screenshot of a calculator in your work rather than typing out the details.
B) Approximate ∫0^0.56 e^-x^2 dx by using a finding a Taylor series for e^-x^2, integrating, then evaluating the degree 9 Taylor polynomial.
C) Compare each result to the äctualïntegral obtained from a calculator. Which is more accurate? Which was easier to compute?
Upload your work here. You can use Insert->Image to add pictures, or Insert->Attach File to add other files.

Added by Derek G.

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