2. Suppose we want to compute the arclength of y = ln x from x = 1 to x = 3. (a) Write out the integral corresponding to the arclength. Don't try to solve it (it is very difficult to do using the FTC). (b) Write the values of the integrand (function inside the integral sign) for x = 1, 1.5, 2, 2.5, and x = 3 in a table, rounded off to the nearest thousandth. Then, approximate the arclength using the trapezoid rule and Simpson's rule using these five points. (For the sake of comparison, here is the exact answer, thanks to an integral calculator:) In (√10+1)-In (√/10-1) - In (√2+1) + In (√2-1)-2√/10 + 2² 2 Approximation: 2.301987534577569
2. Suppose we want to compute the arclength of y = ln x from x = 1 to x = 3. (a) Write out the integral corresponding to the arclength. Don't try to solve it (it is very difficult to do using the FTC). (b) Write the values of the integrand (function inside the integral sign) for x = 1, 1.5, 2, 2.5, and x = 3 in a table, rounded off to the nearest thousandth. Then, approximate the arclength using the trapezoid rule and Simpson's rule using these five points. (For the sake of comparison, here is the exact answer, thanks to an integral calculator:) In (√10+1)-In (√/10-1) - In (√2+1) + In (√2-1)-2√/10 + 2² 2 Approximation: 2.301987534577569
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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Transcribed Image Text:2.
Suppose we want to compute the arclength of y = ln x from x = 1 to x = 3.
(a) Write out the integral corresponding to the arclength. Don't try to solve it (it is very difficult to
do using the FTC).
(b) Write the values of the integrand (function inside the integral sign) for x = 1, 1.5, 2, 2.5, and x = 3
in a table, rounded off to the nearest thousandth. Then, approximate the arclength using the
trapezoid rule and Simpson's rule using these five points.
(For the sake of comparison, here is the exact answer, thanks to an integral calculator:)
In(V10 + 1) – In(V10 - 1) – In(v2 +1) + In(v2 – 1) – 2/10 + 2
2
Approximation:
2.301987534577569
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