Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors for n = 4, 8, 16, and 32. The exact value of the integral is given for computing the error. x/8 T 0 8 sin 4x dx=2

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors
for n = 4, 8, 16, and 32. The exact value of the integral is given for computing the error.
*/8
S
0
8 sin 4x dx = 2
Complete the table below for the Midpoint Rule.
4
8
Midpoint Rule
2.0129
2.0032
Absolute Error
0129
.0032
(Round to four decimal places as needed.)
Complete the table below for the Trapezoid Rule.
4
8
n
n
Trapezoid Rule
Absolute Error
(Round to four decimal places as needed.)
16
2.0008
.0008
16
32
2.0002
.0002
32
Transcribed Image Text:Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors for n = 4, 8, 16, and 32. The exact value of the integral is given for computing the error. */8 S 0 8 sin 4x dx = 2 Complete the table below for the Midpoint Rule. 4 8 Midpoint Rule 2.0129 2.0032 Absolute Error 0129 .0032 (Round to four decimal places as needed.) Complete the table below for the Trapezoid Rule. 4 8 n n Trapezoid Rule Absolute Error (Round to four decimal places as needed.) 16 2.0008 .0008 16 32 2.0002 .0002 32
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