The sine-integral function, shown below, is one of the many functions in engineering whose formulas cannot be simplified. There is no elementary formula for the antiderivative of ( sin t) / t. Complete parts (a) through (c) below. sint dt t Si(x) = Click the icon to view more information. 2 a. Use the fact that |f(4)|<1 on 0, sint dt is to give an upper bound for the error that will occur if Si %3D estimated by Simpson's Rule with n= 4. (Round to five decimal places as needed.) b. Estimate Si by Simpson's Rule with n = 4. 2 (Round to five decimal places as needed.) c. Express the error bound you found in part (a) as a percentage of the value you found in part (b). % (Round to three decimal places as needed.)
The sine-integral function, shown below, is one of the many functions in engineering whose formulas cannot be simplified. There is no elementary formula for the antiderivative of ( sin t) / t. Complete parts (a) through (c) below. sint dt t Si(x) = Click the icon to view more information. 2 a. Use the fact that |f(4)|<1 on 0, sint dt is to give an upper bound for the error that will occur if Si %3D estimated by Simpson's Rule with n= 4. (Round to five decimal places as needed.) b. Estimate Si by Simpson's Rule with n = 4. 2 (Round to five decimal places as needed.) c. Express the error bound you found in part (a) as a percentage of the value you found in part (b). % (Round to three decimal places as needed.)
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 46SE: Near the surface of the moon, the distance that an object falls is a function of time. It is given...
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![The sine-integral function, shown below, is one of the many functions in engineering whose formulas cannot be
simplified. There is no elementary formula for the antiderivative of (sin t) / t. Complete parts (a) through (c) below.
sint
dt
Si(x) =
Click the icon to view more information.
2
a. Use the fact that |f(4)|<1 on 0,
2
sint
dt is
t
to give an upper bound for the error that will occur if Si
estimated by Simpson's Rule with n = 4.
(Round to five decimal places as needed.)
by Simpson's Rule with n = 4.
2
b. Estimate Si
(Round to five decimal places as needed.)
c. Express the error bound you found in part (a) as a percentage of the value you found in part (b).
%
(Round to three decimal places as needed.)
More info
The values of Si(x) are readily estimated by numerical integration. Although the notation
does not show it explicitly, the function being integrated, shown below, is the continuous
extension of ( sin t) /t to the interval [0,x]. The function has derivatives of all orders at
every point of its domain. Its graph is smooth, and you can expect good results from
Simpson's Rule.
sint
f(t) =
t#0
Si (x) =
sin t
di
t
sin t
V =
1,
t= 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b5d3f26-cda5-43e5-8223-bfa02258241c%2F4ac2a2ca-7fb5-46dc-8203-29a152f99793%2Fhn9jiq9_processed.png&w=3840&q=75)
Transcribed Image Text:The sine-integral function, shown below, is one of the many functions in engineering whose formulas cannot be
simplified. There is no elementary formula for the antiderivative of (sin t) / t. Complete parts (a) through (c) below.
sint
dt
Si(x) =
Click the icon to view more information.
2
a. Use the fact that |f(4)|<1 on 0,
2
sint
dt is
t
to give an upper bound for the error that will occur if Si
estimated by Simpson's Rule with n = 4.
(Round to five decimal places as needed.)
by Simpson's Rule with n = 4.
2
b. Estimate Si
(Round to five decimal places as needed.)
c. Express the error bound you found in part (a) as a percentage of the value you found in part (b).
%
(Round to three decimal places as needed.)
More info
The values of Si(x) are readily estimated by numerical integration. Although the notation
does not show it explicitly, the function being integrated, shown below, is the continuous
extension of ( sin t) /t to the interval [0,x]. The function has derivatives of all orders at
every point of its domain. Its graph is smooth, and you can expect good results from
Simpson's Rule.
sint
f(t) =
t#0
Si (x) =
sin t
di
t
sin t
V =
1,
t= 0
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